Conte's job is under real threat following a woeful 4-1 defeat at Watford on Monday.
But Cahill said: "Whatever is decided, the players have to take responsibility. The manager has done an absolutely unbelievable job.
"This is the worst I've felt for quite a while. 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."