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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.
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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.