Jesus Navas set the tone for a one-sided afternoon at the Etihad Stadium, scoring after just 13 seconds following Hugo Lloris' awful mistake.
Sandro scored an own goal, with Sergio Aguero netting either side of the interval, before Alvaro Negredo added another and Navas wrapped up a comfortable win in stoppage time as Spurs slipped to ninth in the Barclays Premier League.
"To lose 6-0 is extremely embarrassing," Villas-Boas said. "We have high expectations for the season and losing to a rival by that scoreline is always difficult.
"A defeat like this tends to stick more to your career than the good things you achieve.
"Our game plan, our confidence and motivation was affected after we suffered a goal in 13 seconds.
"It is a bad moment. We have to be ashamed of the result."
After spending £108million during the summer, much of it admittedly generated by the world-record sale of Gareth Bale to Real Madrid, Villas-Boas knows he is under pressure to produce positive results.
With only nine league goals - the same number as Fulham - it is easy to see where Tottenham's problems lie, even though their difficulties on Sunday afternoon were at the other end of the field.
"City made the most of their opportunities. We didn't make the most of any opportunities we had," Villas-Boas said.
"We reacted well to conceding that first goal, but the second and third straight afterwards put us in a very poor position to come back."
The straw Villas-Boas was able to clutch at is that, despite collecting just a single point from their last three games, Tottenham are still only four adrift of second-placed Liverpool.
"The only thing that is astonishing in this league is that surprising results can happen," the Portuguese said.
"City are on four defeats. We are on four defeats, at such an early stage in the season.
"The December and January results will be vital in how the league will finish.
"At the moment you can be third or ninth. That is the reality."
So desperate has Tottenham's search for goals become that Villas-Boas has even welcomed former City striker Emmanuel Adebayor back into the fold for the first time this season, although his half-time introduction had no impact.