The European champions were overpowered by their League One opponents during the opening 45 minutes of the fourth-round tie at Griffin Park, which saw interim manager Benitez once again bear the brunt of fan frustration.
But Chelsea came out with renewed purpose after going into the break 1-0 down and, despite falling behind again after equalising, they snatched a barely-deserved replay.
Benitez went into Sunday’s game having given his strongest indication yet that he wanted the manager’s job full-time, something that would go down like a lead balloon with supporters who chanted, “You don’t know what you’re doing”, yesterday.
Those sentiments were not shared by Chelsea’s squad, according to defender Cahill, who insisted he and his teammates demonstrated as much at Griffin Park.
“Yes, of course,” he said.
“There is a lot of pressure from the fans but we needed to just try to do the job. In the end, we grafted it out on a horrible day and we now need to show our quality at home.
“It was the character we needed to dig in and just get the result. There were a few words said in the dressing room from Rafa and then between the players.
Everyone knew we were below par. We spoke about that and we needed to do something about it in the second half,” he added.
An FA Cup replay compounded Chelsea’s fixture pile-up, which has already seen them play 40 matches this season and will end with them completing a minimum 58 and maximum 71.
Benitez admitted many of his players were running on empty, especially with injuries, suspensions and international call-ups all coming at the same time.
David Luiz (ankle) and Petr Cech (leg) remained doubts for Wednesday’s Premier League game at Reading, with Eden Hazard already banned.