And for all the plaudits applied to their great La Liga rivals Barcelona, the praise for the continuing excellence and endurance of Bayern Munich and Juventus and the continuing defiance over the odds of Atletico Madrid,  they remain the continent's pre-eminent footballing force.
The great Cristiano Ronaldo, when analysing his own achievements, underlined it by saying: "The numbers don't lie."
And the same applies to Real Madrid - the 4-1 victory on Saturday sealed their third Champions League win in four years. Those numbers do not lie either.
So why are Real Madrid currently in a league of their own?
"Those who always criticise Cristiano are going to have to put their guitar back in its case."
These are the third-person words of Ronaldo after his fourth Champions League triumph, his third with Real after winning with Manchester United in Moscow in 2008.
And even after scoring his 600th career goal, adding polish to a Champions League record that now reads 105 goals in 140 games and scoring in his third final, the dwindling band that continues to criticise Ronaldo is increasingly out of tune.
The Portugal captain has now scored at least twice as many Champions League goals as any other other player in the quarter-finals (20), semi-finals (13), and finals (four).
The criticism usually revolves around Ronaldo's ego and personality but - to twist an old Sir Winston Churchill quote about his predecessor and successor as prime minister Clement Attlee - he may be immodest but he has got plenty to be immodest about.
After embracing his Old Trafford mentor Sir Alex Ferguson backstage and then receiving the man of the match award from him, this fiercely dedicated and consummate professional reflected on his feats at 32, an age when many players are feeling the tap on the shoulder from Father Time.
He said: "I will now have two or three days off, then it is World Cup qualifiers with Portugal before the Fifa Confederations Cup. It is a long season but I am motivated.
"My age is just a number. I feel like a young boy."
Media playback is not supported on this device
Joyous news for all at Real Madrid, where occasionally he has not felt unconditional love from the inhabitants of the Bernabeu, and ominous words for those hoping to unseat them as European football's superpower.
Real Madrid have world class sprinkled throughout their team, from Sergio Ramos in defence, through Toni Kroos and Luka Modric in midfield, to Ronaldo.
It is, for all those riches, Ronaldo who currently makes Real a cut above the rest and means they will be strong candidates for a 13th Champions League next season.
Here he showed that petulant side in the first 20 minutes before emerging, yet again, as the most significant figure in a game of world-class quality.
The usual debate has already begun about who is the better between Ronaldo and Barcelona forward Lionel Messi. It is simpler to just enjoy two of the all-time greats - but this season has belonged to Ronaldo and his performance in Cardiff confirmed it.
The forces of personality inside Real Madrid's dressing room can make it a combustible place - but the bad news for their rivals is that the sheer stature and knowledge of coach Zinedine Zidane provides the glue that has brought unity.
This quietly spoken character commands instant respect from his playing days when he was a World Cup winner with France in 1998, won Euro 2000 and acquired legendary status at Real Madrid when he was man of the match in the 2002 Champions League final against Bayer Leverkusen at Hampden Park. There he scored the winner with one of greatest goals seen in one of these showpiece games, hooking a left-foot volley over his shoulder from a Roberto Carlos cross.
Zidane's coaching career at the Bernabeu was something of a slow burner, moving from coach of Real Madrid Castilla, the club's "B" team to taking over from the sacked Rafael Benitez in January 2016.
The results have been extraordinary as Zidane moves seamlessly from greatness as a player to history-making coach.
Since taking charge he has won the Champions League in successive seasons, making Real the first club to achieve this, brought La Liga back to the Bernabeu for the first time in five years and has also secured the Super Cup and World Club Cup.
Zidane is the first coach to win Europe's elite club competition back-to-back since Italian Arrigo Sacchi with AC Milan in 1989 and 1990, and while he may not exactly be a reluctant hero, he has brought an understated sprinkling of stardust to the "Galacticos".
He is clearly proud to manage Real, saying: "I am a man of this house."
And what he brings, what he brought to Cardiff, was the authority that comes from being one of the best, a man who can speak on equal terms to modern greats such as Ronaldo. He can look them in the eye and they know he has been to the same places as them.
In that respect, the 44-year-old is the perfect man for Real's present and, when it comes to keeping them ahead of those who want to topple them, the future.
Ronaldo was full of praise for Zidane's half-time address after Real had struggled to subdue Juventus in the first 45 minutes.
"Zinedine Zidane gave us a really positive half-time team talk," he said. "He really believed in us."
Success for a Real Madrid coach usually only stretches as far as the next game, but Zidane is in an impregnable position.
And he is ready for the next challenge.
"This is a truly historic day for all Real Madrid fans, the players and myself - but we know how things are," he said.
"We know it is going to be even more difficult to win but we are now going to work very, very hard to win once again."
While the Premier League's own Champions League qualifiers Chelsea, Tottenham, Manchester City, Liverpool and Manchester United brace themselves to wield the chequebook in readiness for next season, a glance at Real Madrid's squad strength may cause some sleepless nights.
Let's leave those who actually started in Cardiff to one side - the names on Real Madrid's bench are enough to be going on with.
Zidane was able to set aside concerns about Gareth Bale's ability to last 90 minutes on his return to Wales because he had a player of the quality of Isco, the world-class Wales forward being introduced as a late substitute.
Bale was joined on the bench by 24-year-old Alvaro Morata, coveted by Chelsea and Manchester United and yet unable to make Real's first-choice side for a Champions League final.
Marco Asensio, at just 21, made his contribution with a goal as a midfield substitute, while 23-year-old Croatia midfielder Mateo Kovacic did not get any game time.
And, just as significantly, were those who did not make the matchday squad. Pepe and James Rodriguez, the latter touted as potentially a marquee signing for some of the Premier League's elite clubs, did not even get to change out of their club suits.
Place this next to the class in Real's side - and here you can simply list Saturday's starting XI - and the scale of the task of overtaking the Bernabeu giants becomes clear.
Real have superstar players and a superstar coach - and it may all have come together at the perfect time for them to extend their rule of European football.
Barcelona, stung by watching Real win La Liga and the Champions League, are currently in a period of transition.
Ernesto Valverde, formerly of Athletic Bilbao, has replaced Luis Enrique as manager, and will be under orders to reverse the current trend.
Lionel Messi, Neymar and Luis Suarez represent a world-class attacking trio but this is a side in need of renewal.
There is still an over-reliance on the Argentine while the great midfielder and leader Andres Iniesta is now 33 and will soon have to be replaced.
In this environment, Real can be guaranteed to be ruthless when it comes to squad strengthening.
Zidane swatted away questions about Bale's future but, as Sir Alex Ferguson once said about Manchester United, this is a bus that waits for no-one.
The likes of Morata and, far more likely, Rodriguez will go but Real are already being ominously linked with the sort of talent that will add even further lustre to this great side.
Manchester United goalkeeper David de Gea is consistently linked with a return to Madrid, this time with Real, while they are already in pole position to sign the prodigy with all the gifts to be a "Galactico" of the future, Monaco's 18-year-old France forward Kylian Mbappe.
Mbappe may well cost a world-record transfer fee - but Real have never blinked in the face of that before and in the afterglow of yet another Champions League triumph they will want to strike another footballing and psychological blow to those they consider their closest rivals.
Ronaldo's astonishing 12 months in photos
Real Madrid's status as Europe's most successful club was confirmed as their ruthless Champions League final win over Juventus gave them their 12th win in this competition.