The Portuguese boss says victory over the Toffees is 'rewarding' for the Blues and insists his squad will not be tired by the time its game against Arsenal comes around.
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."
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 its opposition of the ball when under pressure, while admitting that his side has spurned opportunities to secure a more comfortable triumph.
"It was good," Villas-Boas said. "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."
When asked whether he had any complaints over the penalty awarded against Chelsea, Villas-Boas laughed and went on to say that the 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."