The England international defender was left out of the squad to travel to Merseyside, as allegations of racism in The Blues 1-0 defeat to QPR at the weekend are currently being investigated by the FA.
After the hard-fought victory, the Portuguese coach admitted the players had their captain in mind.
“The spirit of the players took us through. I think all of the players would like to dedicate the win to John Terry,” Villas Boas told Sky Sports.
Salomon Kalou had given the visitors the lead before Louis Saha forced the game into extra-time, where Daniel Sturridge converted the winner for the London outfit.
With Toffees midfielder Royston Drenthe and Chelsea’s goalkeeper Ross Turnbull both dismissed, the away team’s trainer was delighted to progress through to the next stage.
“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.
“When you triumph in a game like this, you cannot toast the individuals you have to toast the collective spirit of a squad that once again goes down to 10 men.
“We wanted to avoid it but it happened and we saw the game through,” he concluded.
Chelsea have no respite as the fixtures come thick and fast in November, with Arsenal their next opponents at Stamford Bridge this weekend.
By Gareth McKnight