Blues boss Villas-Boas admitted if his side were to stand any chance of overhauling the Barclays Premier League leaders, they needed to strike while City were in their worst shape of the season.
Roberto Mancini's men have lost three of their last four games in all competitions to offer Manchester United and Tottenham real hope of beating them to the title.
Fourth-placed Chelsea will need City's 2012 slump to continue to close the 11-point gap between the sides, while embarking on the kind of winning run that has so far eluded them this season.
Villas-Boas said: "The problem is you have to show it on the pitch.
"At the moment, we have exhausted ourselves in words.
"It's time for us to get a practical run of victories to make our title challenge together. We are trying to begin that."
It is something Spurs have managed with aplomb since losing their opening two games of the campaign to the Manchester clubs.
Harry Redknapp's men beat Everton on Wednesday night to justify claims they are genuine title challengers, while also cementing their new-found status as London's pre-eminent club.
That tag has belonged to Chelsea for most of the past decade and it was not one Villas-Boas was ready to concede.
"They've overtaken us in the Premier League table this season, for sure," he said.
"Both clubs have fantastic history, but there is no comparison between the clubs over the last 10 years."
Villas-Boas felt Spurs' ascent could work in favour of the chasing pack, with them, City and United all knowing a slip-up might cost them dearly.
He said: "The fact there are three teams so close together, it means a couple can lose points bearing in mind recent happenings - City losing three in four, and United trying to find that consistency like us.
"Anything can happen. Eight points (to Spurs) is still a distance you can turn around.
"We have a job to do to prove the doubters wrong. We have to do that on the pitch, not with words."
Chelsea also need to act off the field, with Villas-Boas having already admitted his current squad is not good enough to win the league.
He was planning to add Gary Cahill and one other player during the January transfer window, with speculation rife about the identity of the second signing.
Reports on Thursday suggested it could be Lille star Eden Hazard but Villas-Boas insists Chelsea have made no approach for the highly-rated Belgian.
He said: "He's an excellent young talent that exploded last year in Lille's double-winning trophy season.
"But there is no official approach whatsoever."
There has also been plenty of talk of departures on top of those of Alex and Nicolas Anelka.
Villas-Boas rejected any suggestion Frank Lampard could be sold amid reports of a strained relationship between manager and player.
"He's going to be here for sure," Villas-Boas said.
It was a similar story with the soon-to-be out of contract Didier Drogba and Salomon Kalou, who are both on African Nations Cup duty with the Ivory Coast.
"They will return to this club from the African Nations and hopefully we will hold on to them until the end of the season," Villas-Boas said.
"That's our intention, and I think their willingness as well."
Two players definitely on the way out of Stamford Bridge on loan deals are Josh McEachran and Gael Kakuta.
Villas-Boas confirmed McEachran would join Swansea until the end of the season after Saturday's Sunderland match, with Kakuta putting the final touches on his move to Dijon - who jumped the gun by announcing his arrival on Wednesday.