The Spain international was handed a three-match ban, the first game of which was served in his team's 1-1 draw against Manchester City, for violent conduct.
Costa appeared to stamp on Can's ankle – one of several confrontations he had during Chelsea's League Cup semi-final second-leg win over Liverpool.
"As far as what happened on Tuesday, the main thing is when I get home I can go home and I can go to sleep knowing that I’ve not done anything wrong, because I never meant to do that and it was not on purpose," Costa said.
"And you can clearly see that on the video. But it is a suspension. I have to accept that, I have to take it.
"Obviously I feel sad because I’m not going to be able to help the team, to play. But I have accept it and respect it."
Costa's confrontational and physical style has been questioned, but he has scored 17 goals – a league-high – for his table-topping team.
“I’m not saying I’m an angel. I’m no angel. You can see that," Costa said.
"But every time I play I will play the same way because that’s the way I am.
"That’s what I need to do in order to support my family. That’s my bread and butter, also that’s what I need to do for this club and for the fans of this club, for the supporters and for all the people involved in this club.
“On the pitch I will always be like that. That’s my character and I will always compete and compete - always. I’m a different guy off the pitch."
