The Spaniard has come under frequent scrutiny since being placed in charge of the Blues in November, and didn't help silence his critics after his side drew 2-2 with League One Brentford in the FA Cup on Sunday.
However, having gone twice gone behind in the match, Cahill is adamant that the club's comeback proves that they are behind the boss.
"The character we showed in the second half shows we're playing for the manager," Cahill said in The Mirror.
"He's under a lot of pressure from the fans, but we have grated out a result in horrible conditions.
"The first half wasn't good. We could blame the pitch and that we couldn't see anything in the sunshine. But we shouldn't as we were really sloppy and off the pace."
Chelsea travel to Reading in the Premier League on Wednesday.