The 34-year-old, who will leave Liverpool for LA Galaxy at the end of the season, came on as a second-half substitute but was sent off just 40 seconds after the interval for a stamp on Ander Herrera.
Gerrard came out and took the blame for the defeat after the match, while Mignolet confirmed that the retired England skipper was apologetic in the dressing room after the final whistle.
Mignolet: Gerrard apologised to us
"That's what he is about," Mignolet was quoted as saying by ITV Sport. "He spoke to the team after the game inside the dressing room and what was said exactly shall stay in there, but it shows who and what he is off the pitch."
Gerrard admitted he needed to accept the decision, but hinted that he was less than impressed with the initial challenge from Herrera.
Gerrard: I need to accept it
"I need to accept it; the decision was right," Gerrard told Sky Sports, according to the BBC. "I've let down my team-mates and the fans."
"I take full responsibility. I don't know what caused it. Probably just a reaction to the initial tackle," he added. "I shouldn't say more about it really. I've just come out here to apologise to the dressing room and supporters."
Dreadful 12 months for Gerrard
It was yet another dreadfully disappointing incident for Gerrard, who has been through so much professional torment over the past 12 months.
His untimely slip against Chelsea was the iconic image of the 2013-14 Premier League campaign. It was a crucial moment towards the end of the season, and one which possibly cost Liverpool the chance to become champions of England for the first time since 1990.
A month later it was Gerrard's header which inadvertently led to Luis Suarez scoring the goal for Uruguay which effectively knocked England out of the 2014 World Cup finals in Brazil.
Gerrard looked similarly crestfallen on Sunday afternoon - and after so much personal heartache it's little wonder why he has made the difficult decision to quit Anfield and the England national team in order to wind down his career in Major League Soccer.
Gerrard deserves to end Liverpool career on a high
Gerrard is undoubtedly one of the finest players in Liverpool's history and it would be fitting if he ends his career with the Merseyside outfit by winning the FA Cup and inspiring the Reds to a top-four finish.
But while the former remains a distinct possibility, Liverpool now have their work cut out to finish inside the top four as a direct result of Manchester United's recent resurgence.
Liverpool fans: do you forgive Steven Gerrard for his foolish red card against United? Let us know by leaving a comment in the box below!