Costa scored 20 league goals last term as Chelsea went on to win the title with a comfortable eight-point margin but has struggled so far this campaign.
The Spain international has a solitary league goal and has been in the news for all the wrong reasons, including being retrospectively banned for violent conduct during the 2-0 win over Arsenal on Sept. 19.
"We know we're not in the form we were supposed to be at the beginning of the season. I'm going to be very honest, maybe a few weeks ago, I was not on top of my game. At least physically," Costa was quoted as saying by the British media.
"I got injured at the end of last season and then I went on holiday. When I came back ... I was a little bit overweight. That affected my game.
"You can be selfish and blame it on the manager but I'm not going to do that. I'm responsible 100 percent, and so are the other guys," the 27-year-old added.
Costa joins a host of senior players, including John Terry and Cesc Fabregas, who have backed Mourinho in what the Portuguese has described as "worst period in my career".
The Blues have been woeful defensively, conceding 17 league goals already. They let in only 32 league goals last season.
Defender Gary Cahill also continued the theme of presenting a united front, backing Mourinho to turn things around.
"I think in terms of backing the manager, of course we all back him, of course we are all around him," Cahill said.
"Dare I say he doesn't even need backing, when you've done so much in the game, not just in this league but in other leagues too.
"It is obviously nice to have that and he certainly has it from the players and the club," he added.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
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