The League One side beat Championship club Charlton in the last round.
"We'll be going into every game to win, but we've got to be realistic as well," Wright told BBC Essex.
"Both sides are flying at the top of the Premier League, they're aiming for the top four and maybe even the title."
Fourth-placed Spurs and second-placed Leicester drew 2-2 at White Hart Lane on Sunday, and the winners of the replay will travel to Colchester at the end of this month.
"We need to make sure we don't get overawed by the occasion and give a real good account of ourselves, because it is the FA Cup and you never know," added Wright, who became the club's assistant manager when Kevin Keen was appointed as U's boss last month.
"They'll be coming to our place and the pressure will be all on either team that gets through.
"We can set ourselves up and really enjoy the occasion and hopefully cause them a number of problems."

The 22-year-old, who won the English Amateur Championship last summer, had previously said she would stay amateur.
Giles. who is the first golfer to win all three major English women's amateur titles, has applied for the Access Series of the European Ladies Tour.
"This season just gone I achieved everything I wanted to achieve in the amateur game, so I'm ready to take on the pro game now," she said.
"I'm hoping to eventually end up in America on the LPGA tour, that's where everyone really aims to get to, that's where the best competition is, that's where the best golf courses are and it would be a really awesome experience to go out there."
Giles says she is inspired by Charley Hull, who like Giles had an impressive amateur career before turning professional at the age of 16.
"I'd love to play in the Solheim Cup one day, that would be the aim," she added to BBC Radio Cornwall.
"That's what Charley Hull's done in the last few years, she was an amateur playing in the same stuff I was playing in and now she's doing really well in America and played two Solheim Cups."

The new limits come as the scandal-hit Japanese carmaker prepares to appoint Carlos Ghosn as chairman.
The firm wants to raise the cash limit on executive pay from 960m yen (Â£6.7m, $8.4m) to 2bn yen. There could also be non-cash rewards worth 1bn yen.
The new salary caps need approval by shareholders.
They are due to vote on that at an extraordinary meeting on 14 December.
Shareholders will also be asked to approve the appointment of Nissan and Renault boss Carlos Ghosn as chairman, and three other new executives with experience at Nissan.
If approved, the total annual pay packages of all 11 executives on the company's new board could amount to more than $290m.
Mitsubishi Motors says the new salary caps are designed to attract outside talent to the company.
Its reputation was hit badly after it admitted in April to falsifying the fuel efficiency of several models.
The admission led to a suspension of sales of the vehicles and prompted a sharp drop in Mitsubishi Motors' share price.
Mitsubishi has suffered heavy losses resulting from the scandal. It has forecast a net loss of 145bn yen for the current financial year.
In May, Nissan helped to bail out Mitsubishi Motors by taking a 34% stake in its smaller rival.
Colchester United assistant manager David Wright says the club must be realistic about their chances of overcoming Tottenham or Leicester City in the fourth round of the FA Cup.
[NEXT_CONCEPT]
Cornwall golfer Sammie Giles says she is planning to turn professional.
[NEXT_CONCEPT]
Mitsubishi Motors is proposing higher salary caps that could triple the annual pay packages of its top executives.