Carragher claimed the loss of the two influential figures has had a big impact on the Stamford Bridge club.
“There's no doubt they lost something with captain John Terry going, with what he was like around the training ground and in the dressing room, and of course they miss Costa," he said.
“There are few strikers who can do what he does.
"However, while people say Conte could have managed that situation better, Costa caused a lot of problems and it will have been difficult for the manager to forget about him not wanting to play in a title run-in.
“If you're in Conte's position, you're not going to accept that. It's then up to you to replace him with quality."