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Marshall is the third player to refuse to stand for the anthem since Colin Kaepernick did so last month in protest at what he sees as racial injustice.
"I feel like this was the right thing to do," said Marshall.
Broncos beat Carolina 21-20 in a re-run of February's Super Bowl 50.
At a pre-season game in August, San Francisco 49ers quarterback Kaepernick chose to remain seated while the national anthem was played.
He said he would not "stand up to show pride in a flag for a country that oppresses black people and people of colour".
Kaepernick's team-mate Eric Reid joined him in not standing during the team's final pre-season game while Seattle Seahawks' cornerback Jeremy Lane stayed seated ahead of a game with Oakland.
Marshall, a college team-mate of Kaepernick at Nevada, told NFL.com: "The message is I'm against social injustice. I'm not against the military or police or America at all.
"I knew what territory it came with, and I decided to do it. I feel like this is the right platform. This is our only platform to really be heard."
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The NFL has previously said players are "encouraged but not required" to stand during the anthem.
The Panthers took a 17-7 lead into the fourth quarter of the first Super Bowl rematch to start a season since 1970, but running back CJ Anderson scored two touchdowns as the Broncos edged ahead.
Graham Gano's field goal pulled the Panthers within a point, but he then missed his next attempt from 50 yards with four seconds left as Denver held on.
How to follow the 2016 NFL season on BBC TV and RadioNFL 2016: Kaepernick, Brady & Beckham Jr - all you need to know for new season

The 40-year-old woman died from her injuries following the fall at Clarendon Court, Southsea, Portsmouth, on 12 February.
A 46-year-old man, from Southsea, who was arrested on suspicion of murder, has been released with no further action to be taken, police said.
Hampshire Constabulary added it was preparing a file for the coroner.

The Somali-born author was to appear on Australian TV on Monday before starting her tour, titled "Hero of Heresy".
But she pulled out due to "a number of reasons including security concerns", event organiser Think Inc said.
Ms Hirsi Ali has faced death threats in the past.
"[She] hopes to be able to return to Australia in the not too distant future," Think Inc said in a statement.
About 2,000 tickets had been sold for the speaking events in Brisbane, Melbourne, Sydney and Auckland.
She was granted asylum in the Netherlands in 1992, and was elected as an MP in 2003.
Ms Hirsi Ali rose to international attention in 2004 as the writer of a controversial film on violence against Muslim women, Submission, after her collaborator, filmmaker Theo van Gogh, was murdered by a radical Islamist.
Having received repeated death threats over her challenges to Islam's treatment of women, Ms Hirsi Ali spent time living under 24-hour police guard.
She then moved to the United States, where she has maintained a high profile.
In an article for the Hoover Institution last month, Ms Hirsi Ali described what she called "political Islam" as being not just a religion but "a political ideology, a legal order, and in many ways also a military doctrine associated with the campaigns of the Prophet Muhammad".
Nearly 400 people had signed an online petition opposing Ms Hirsi Ali's visit to Australia and New Zealand.
"Against a backdrop of increasing global Islamophobia, Hirsi-Ali's divisive rhetoric simply serves to increase hostility and hatred towards Muslims," the petition said.
Protests had been planned at locations where she was speaking, and people who bought tickets were told their bags would be searched.
Think Inc said all ticketholders would receive refunds.

The 25-year-old joined the Shrimpers in the summer after a trial, having not played a first-team game since November 2014 while at Blackpool.
The former Newcastle and Swindon forward has since scored twice in nine Southend appearances.
Phil Brown's side are undefeated in any match Ranger has started, winning five and drawing three of the eight games.
Denver linebacker Brandon Marshall kneeled in protest during the American national anthem prior to the Broncos' victory over the Carolina Panthers in the opening game of the new NFL season.
[NEXT_CONCEPT]
The death of a woman who fell from the window of a third-floor flat is no longer being treated as suspicious.
[NEXT_CONCEPT]
A former Dutch MP and prominent critic of conservative Islam, Ayaan Hirsi Ali, has cancelled a speaking tour of Australia and New Zealand citing security concerns.
[NEXT_CONCEPT]
Southend United striker Nile Ranger has signed a new three-and-a-half year contract with the League One club.