Gerrard saw red less than a minute after coming on at half-time in a crucial clash in the fight for UEFA Champions League qualification for stamping on the leg of Ander Herrera.
The midfielder looked to have won the ball in the initial challenge, but a rush of blood to head left his side with a mountain to climb after United had taken the lead in the 14th minute through Juan Mata.
Mata doubled United's lead with a spectacular scissor-kick in the 59th minute, with Daniel Sturridge pulling one back before Wayne Rooney missed a late penalty following Emre Can's foul on Daley Blind, leaving Gerrard to lament what might have been if not for his moment of madness.
He told Sky Sports: "I need to accept it, the decision was right, I've let my team-mates and the manager down today and most importantly the supporters.
"I've been in the game long enough to know that when you've done something like that... I take full responsibility for it.
"It was just a reaction to the initial tackle, I don't think I should say too much more, I came out to apologise to everyone in the dressing room, the supporters. I take responsibility for the result."
Gerrard's former Liverpool team-mate Jamie Carragher felt Brendan Rodgers' initial decision to leave Gerrard on the bench had a part to play in the dismissal.
Carragher said: "Watching the first half from the bench he'd have been frustrated. He'd have been thinking 'why am I not playing, why am I not on the pitch?'
"He's an emotional player. When he's done well it's with his heart; Istanbul [in the 2005 Champions League final], the FA Cup final [in 2006].
"On the flip side, four of his seven red cards have come against Everton and Manchester United. The emotion has contributed to the red cards."
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