The European champions were overpowered by their npower 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 the 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".
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."
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.
They played 61 en route to Champions League and FA Cup glory last term and fatigue may well have played a part in them surrendering an unprecedented five trophies since then.
Cahill said: "Having a replay is not ideal. There are so many games, it feels like you're only just recovering and then there is another game again.
"You're trying to get your full recovery in before the next game and it's hard when there are not many days to do that. Sometimes, you do feel leggy."
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 Barclays Premier League game at Reading, with Eden Hazard already banned.
Hazard could also miss the Brentford replay if the Football Association extend his three-match ban for kicking out at a ball boy to five games.
That would give Brentford even more hope of completing an unlikely giant-killing at Stamford Bridge on February 17.
Bees hero Harry Forrester, whose penalty almost secured him a place in FA Cup folklore, said: "It's not impossible. I think people would've said drawing here was impossible, to get a result against the European champions."
The striker revealed he had expected more from Chelsea following their Capital One Cup exit, adding: "They went out of the cup at Swansea in the week and we thought we might have got a bit of a backlash."
Instead, Brentford's players were able to boost their own reputations, not least Forrester, who was reportedly watched by West Brom sporting director Dan Ashworth last week.
Forrester - released by Aston Villa in 2011 - insisted he knew nothing of the visit but admitted he was still dreaming of playing in the Premier League.
"You've got to believe," he said. "Obviously, it's everyone's dream to play in the Premier League and I've come down the leagues to learn my trade, and I'm doing that.
"I've got a great manager behind me, great colleagues and a great club.
"I'm at a hungry club that wants success and I'm not somewhere where mediocre is accepted.
"So it's bringing me on as a player and I'm really grateful for that."