Benitez went into Sunday's FA Cup tie at Brentford 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".
Those sentiments were not shared by Chelsea's squad, according to defender Cahill, who insisted he and his team-mates 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 we needed.
"Obviously, we wanted the win but at least we have taken it back to the Bridge and hopefully we can finish the job there.
"Everyone was aware how important the game was. Ideally, we would have gone in at half-time a couple of goals up but that wasn't the case.
"There were a few words said in the dressing room from Rafa and then between the players themselves. Everyone knew we were below par.
"We spoke about that and we needed to do something about it in the second half."