Terry was left out of the Chelsea squad for their Carling Cup fourth round tie at Everton, with the club wary of the defender picking up a fifth yellow card of the season that would have ruled him out of Saturday's meeting with Arsenal.
The England international is under the spotlight at the moment as he waits on a Football Association investigation into allegations he racially abused QPR's Anton Ferdinand during the Blues' 1-0 Premier League loss on Sunday.
Villas-Boas has given Terry his full backing in the wake of the claims, and, speaking after the 2-1 defeat of Everton, he told Sky Sports: "The spirit of the players took us through. I think all of the players would like to dedicate the win to John Terry.
"We deserved it for what we put on as an effort and for the football we played. To be fair, I think we had the worst of the draws. It was a difficult game to play, Everton would like to challenge for silverware and the commitment they had to this competition made them a strong team."