The defending champions are now fourth in the Premier League, 19 points behind leaders Manchester City after a second straight three-goal defeat.
"Whatever is decided, the players have to take responsibility," Cahill said.
"The manager has done an absolutely unbelievable job."
Defender Cahill, who has won the league twice in six years with the Blues, said Monday's defeat at Vicarage Road was the club's "lowest point of the season".
"This is the worst I've felt for quite a while," he told BBC Sport.
"Performance-wise, I didn't recognise us or myself. It was abysmal.
"We just need to keep strong. I've been here before at this club - it's about staying calm. It hurts a lot when you come off after a performance like that."