United and City stormed to the top of the Barclays Premier League before the international break, scoring 13 and 12 goals, respectively, in their opening three games.
Chelsea are just two points adrift of their main title rivals but have managed to score only five times in their three outings, drawing 0-0 at Stoke before struggling to beat West Brom and then Norwich the Saturday before last.
The following day, they watched City romp to a 5-1 win at Tottenham and United annihilate Arsenal 8-2.
But Chelsea manager Villas-Boas was unfazed, saying: "It's good for them. They've gone on to score a lot of goals and it's good for British football.
"We just hope to score one more goal than the opponents."
He added: "Man United played to perfection and managed to score a lot.
"They are, with Man City, leading the table for the Barclays Premier League and we are two behind them.
"We want to grab them.
"Our objective is on shortening distance and not on what the others do in terms of performance."
Chelsea have hardly dazzled since Villas-Boas took charge and the 33-year-old admitted the quality of their game needed to improve ahead of Saturday's trip to Sunderland.
"I think it can be better and our objective is to transform it," he said.
"We have to improve on a weekly basis, on a game-to-game basis.
"It's what people expect from us - to get fluency in the way we play.
"I'm very happy that we have been creating enough chances to win games and this is a good sign for us.
"We just need to improve on the quality and fluency of the game.
"Let's see what kind of response we have now."
Villas-Boas certainly has options to freshen up his attack, with Juan Mata shining as a substitute against Norwich, Daniel Sturridge back from suspension, and Raul Meireles having signed from Liverpool on transfer deadline day.
"Raul was elected by fans last year as the player of the season," said Villas-Boas.
"It was an extremely good deal for us and we are very happy to have him."
He added: "Sturridge never stopped training very, very well since we started the season.
"He's very, very competitive in training.
"You saw the part he could play, not only in pre-season but also at Bolton last year.
"It's a plus that he is on for selection and he can add to the team as well."
It is not just going forward that Chelsea have struggled, with West Brom and Norwich giving their defence more problems than might be expected last month.
But Villas-Boas said: "The team has been sensational throughout.
"Just a reminder that we played seven games in pre-season and only suffered one goal.
"So it would be stupid of me, if we have suffered a couple of goals, to criticise my defence."
Chelsea's defensive travails have coincided with the absence of goalkeeper Petr Cech, who looks certain to be recalled on Saturday after making a swift recovery from his knee injury.
"He is lucky to be with us so quickly," said Villas-Boas, who will also be able to call upon fit-again defender David Luiz.
Villas-Boas believes the advent of midweek football will help his side improve, with the Champions League due to start on Tuesday.
He also feels the closing of the transfer window will allow his players, many of whom were linked with moves, to concentrate solely on Chelsea's upcoming games - until January at least.
He said: "The market is closed now and we have a good three months to focus on the real objectives, and when the window opens, it opens.
"I won't speculate a lot about what is going to happen in January."