Benitez was again subjected to jeers from the away section during the Blues' FA Cup draw at Manchester United, which grew louder in the second half when he substituted Frank Lampard and Victor Moses for Eden Hazard and Mikel.
Those switches helped Chelsea stage a superb comeback to earn a replay, but Mikel says the barracking of Benitez is contributing to their inconsistent form.
"Sometimes it doesn't help when the fans are not happy," said the midfielder. "When you give the ball away there is pressure. This is our job.
"Fans come to watch the football and we have a responsibility to pay them back and make sure we play well. Every game we try to do that, sometimes it works, sometimes it doesn't.
"I have been here for seven years and they (the fans) are fantastic and have always supported us until the end. I hope that continues throughout the season.
"This is when we need them the most. Let's hope we can all go through the rest of the season together. Chelsea fans have always been great and I know they will continue to be great with the players."
Mikel hopes that Chelsea's second-half performance at Old Trafford will instil belief in the squad.
"I hope we can keep this character and momentum going but sometimes it's quite difficult when the season is going like this," he said.
"If you look at the team from last year, we liked to play, to attack, to move forward.
"We liked to have the ball, beat people and create chances and that's exactly what we did in the second half at United.
"Let's hope this game will put us back on a good track and we keep going on from here to end the season very well."