The interim boss has endured heavy criticism during his short stay at Stamford Bridge and recently hit out at supporters for booing him instead of backing the team.
However, Mikel has come out in support of the Spaniard after Chelsea overturned a two-goal half-time deficit to draw 2-2 with United on Sunday.
|8/11||Chelsea are 8/11 with Paddy Power to qualify for the next round of the Europa League
"We came out in the second half and started to show a bit more character, a bit more belief that we could come back into this game. We got the first goal, then the second and we started to believe we could win it."
Chelsea have suffered of late, trailing Steaua Bucharest 1-0 from the first leg of their Europa League last-16 tie while they face a fight with the likes of Tottenham and Arsenal for a Champions League berth next term after their Premier League form faltered.
But Mikel believes that the second-half revival at Old Trafford could kick-start the Blues' campaign heading into the final few weeks and has called on the club's fans to back the team from the stands.
He added: "The character we showed in the second half is something we can keep going. Let's hope this is the performance that puts us back in a good place and we can keep going and end the season well.
"It is natural to lose confidence if things aren’t going well and sometimes it doesn’t help either when the fans are not happy, when they get at you a bit if you give the ball away.
"That brings pressure but this is our job. The fans pay to watch and we have a responsibility to give them something back and make sure we play well. It’s really important for us that they are behind us."