"It was an excellent, positive team performance," said the Portuguese boss of the Blues.
"We dominated the game. In the first half we are one-paced and not incisive.
"We were better in he second half. As a result, we got the goal.
"We gave a good, solid display. QPR made it difficult for us on the counter attack, a result of our mistakes. They were more direct after the goal.
"We are better defensively, since January, we are more organised."
The talking point just before the start was the lack of the pre-match handshake, a decision, Villas-Boas agreed with.
"It was a wise decision not to have the handshake," he said.
"It could have had an impact on the crowd.
"I was informed about 45 minutes before that game the it was not gong to happen.
There was a lot of expectancy and this was a way of avoiding any trouble.
"The players were focused only on the game and emotions were kept low, both sides set out to play football." Speaking about John Terry's performance,
Villas-Boas said: "John Terry was focused on the game, he got his off-field distractions out of his mind."
The Blues move into the 5th round of the FA Cup thanks to a penalty scored by Juan Mata after Clint Hill fouled Daniel Sturridge on 61 minutes.
Villas-Boas had little sympathy for the opposition over what looked a dubious decision.
"QPR were not satisfied, with the penalty," said Villas-Boas. "Mike (Dean) gave it. It was similar to the one Helguson won against us (in the October league match). In that game we also finished the match with nine men.
One sour point from the game was the injury to midfielder Ramires who was carried off on a stretcher.
"It looks like Ramires suffered a medial ligament injury in his knee," said Villas-Boas.
"He will have an MRI scan on Sunday. Hopefully he won't need an operation and could be back within four weeks.