The Londoners played much of the match with 10 men after keeper Ross Turnbull's dismissal, but forced an extra-time winner through Daniel Sturridge after Everton's Royston Drenthe also saw red.
The Portuguese boss was particularly pleased with the character shown to win as his side faced a second game in four days with a numerical disadvantage.
"We were very committed showed strength of character and resilience once again," he told reporters. "We went down to 10 men unfortunately once again and made things even more difficult for us and we are able to triumph in difficulty and this is an extremely good sign for us.
"I think it shows the squad is committed with trophies. To be fair we got one of the most difficult draws, Everton away after a dramatic and motivational win at Fulham.
"Also an Everton, with one of the strongest sides in the Carling Cup, showing they wanted to go through this phase.
"We were able to not only play good football but also to show commitment and desire and physical effort because it’s a game of 120 minutes after a game of 90 minutes with nine men." he continued.
"It shows that we are progressing as a team and it is very gratifying for everybody."
The former Porto man could not hide his delight as Sturridge's late goal sealed victory, and he was pleased with Chelsea's efforts to starve their opposition of the ball when under pressure, while admitting that his side has spurned opportunities to secure a more comfortable triumph.
"It was good," he continued. "To be fair we had good chances to kill off the game but couldn’t find it after getting the first goal strangely.
"We had good chances to kill off the game and then we had to fight because Everton had quality chances and we had 10 men. So we were trying to be as compact as possible but Everton had the desire and motivation and emotionally were on top and we had to hold on until extra time arrived.
"We managed to get things right in possession and what satisfies me more is that the players’ talent comes out in this situation and they were able to find excellent positions with 10 men," he added.
"When the numbers got even they found better spaces and eventually we got the goal we wanted."
When asked whether he had any complaints over the penalty awarded against Chelsea, Villas-Boas laughed and went on to say that tonight's game had been a morale boost after a disappointing weekend result, ahead of a clash with London rivals Arsenal at the weekend.
"It was important to be fair after a defeat that happens like that but we have nothing to say about the effort we put on to try and win at QPR," Villas-Boas continued.
"It was important for us to go back to winning ways and it is more gratifying to do it in this fashion.
"Although the physical effort is immense the emotional benefit that you gain from situations like this is tremendous so it helps us to recover and to be fresh for Arsenal.
"If you see our time-sheet we have minutes spread out for everybody because we have immense talent available and we are able to distribute minutes through everybody in the squad. Physically we won’t have problems."
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