The 34-year-old, who will join the Los Angeles Galaxy at the end of the season, came on at half-time with Liverpool trailing 1-0, only to be sent off after 43 seconds for a crude stamp on United midfielder Ander Herrera.
“I don’t know what caused it. I don’t know. Probably just a reaction to the initial tackle,” Gerrard told Sky Sports.
“I shouldn’t say more about it, really. I’ve just come out here to apologise to the dressing room and supporters.
“I need to accept it. The decision was right. I’ve let down my team-mates and the supporters. I take full responsibility.
“I’ve been in the game long enough (to know what happens) when you do something like that. I take full responsibility.”
Liverpool manager Brendan Rodgers revealed that Gerrard had said sorry to his team-mates after the final whistle.
“Steven apologised to the players and me in the dressing room,” Rodgers said.
“It was probably frustration. We didn’t put a tackle in in the first half, but the players adjusted well.”
Juan Mata scored twice for United, with Daniel Sturridge replying for Liverpool, as Louis van Gaal’s side established a five-point lead over their rivals in the battle for Champions League qualification.
United striker Wayne Rooney also saw a stoppage-time penalty saved by Liverpool goalkeeper Simon Mignolet.
“We kept the ball and created a lot of possibilities; not big chances, but a lot of possibilities to score,” said United manager Van Gaal.
“I said whoever could beat the pressure shall win. Juan Mata was very good. He played always good in my opinion with me, so he’s one of my most constantly playing players.
“But sometimes you also need balance in your team and you have to select other players. Now he has played very well and did this position very well.
“It’s an amazing result for the fans. We now have a gap from positions five, six and seven, which is very important.”
Liverpool defender Martin Skrtel was fortunate to escape unpunished after appearing to stamp on United goalkeeper David de Gea as he chased a through ball at the death, but Rodgers played down the incident.
“I have seen the Martin Skrtel incident,” he said. “The ball was played through, but it probably looks worse in slow-motion.
“It looks like he is trying to get a nick on the ball, to get a toe on the ball, but the ball went into the goalkeeper’s hand. Martin is not that type of player. He was just a fraction out.”