The north Londoners had only conceded six goals in their previous 11 Premier League matches this season but capitulated after going behind after 15 seconds.
Two goals from Sergio Aguero and two for Jesus Navas, as well as one for Alvaro Negredo and Sandro's own goal, made it a miserable afternoon for Portuguese Villas-Boas in his 50th Premier League game in charge of Spurs.
It was Tottenham's heaviest league defeat since a 7-1 loss at Newcastle United in 1996 and Villas-Boas, who led the club to their best ever Premier League points total last season, has the job of trying to arrest a slump that has seen Tottenham fall to ninth in the table.
"We have to be ashamed of ourselves, and react to a defeat like this," Villas-Boas told the BBC.
"It was a difficult start for us. After that, everything you had in mind goes down the drain.
"There are not a lot of positives. We had a good spell of reaction after we suffered the early goals, but everything happened so quickly.
"Our only chance came in the first half. If it goes to 1-1 it is a different game."
Tottenham were undermined by a mistake from keeper Hugo Lloris which allowed Navas to score virtually from the kickoff.
"There is an immediate shock after 15 seconds," the Portuguese former Chelsea coach said.
"The concentration was not there, but the reaction of the players was positive. Everything went wrong for us, every opportunity was a goal and we paid a heavy price, too much for what we deserved.
"City were excellent, and we were extremely poor."
Tottenham now have a trip to the Arctic Circle to clear their heads when they take on Tromso in the Europa League.
"My responsibility is to lift the players, there is always another game coming. We have to give a response in the Europa League."
(Reporting by Martyn Herman; editing by Toby Davis)
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