Carvalho was shown a straight red card by referee Phil Dowd for the 80th minute horror-tackle that could have inflicted serious injury on Agbonlahor.
The Portuguese defender said: "It was never my intention to hurt Gabriel Agbonlahor with the tackle.
"I didn't see him after the game to apologise but I asked for a message to be passed on to him."
Chelsea boss Avram Grant backed Carvalho's claim there was no malice involved in the incident.
He said: "For me what's important is that Carvalho did not intend to hurt the player - I didn't see any intention.
"The red card was the decision of the referee and I respect it. I will look at the incident again."
Aston Villa manager Martin O'Neill maintained the sending off was fully justified.
He said: "It was straightforward red card and Gabriel was the last man, even though he had 40-odd yards to go."