The Blues had to fight back against the League One side at Griffin Park to draw 2-2 and earn a replay in their fourth round tie.
Cahill admits there can be no excuses for such a poor performance despite the difficult conditions, but was happy with the fighting spirit they displayed in the second half.
And he says the squad are fully supportive of Benitez, whose position as interim manager has come under intense scrutiny.
"The character we showed in the second half shows we're playing for the manager," Cahill said in the Daily 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."
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