Things weren't looking good for City when Steven Caulker gave Spurs the lead in the first half, but the hosts improved after the break and were rewarded when Edin Dzeko scored a late winner after Sergio Aguero had equalised.
Villas-Boas explained his game plan after the match but conceded that Spurs had found it difficult to get to grips with their opponents' high defensive line and heavy pressing.
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"The plan before the game was to try and hold on to the ball a bit more, to have possession and try to connect up and link the wingers," he told Sky Sports.
"It was difficult because Manchester City's line was very high and they pushed us very well, so it was difficult to make that second pass in the link up play."
Villas-Boas controversially left Jermain Defoe on the bench despite his hat-trick in midweek against Maribor in the Europa League, but defended his decision to select Emmanuel Adebayor in attack for the fixture.
"In the end, he [Adebayor] had a positive impact regarding the structure we put together," he insisted. "It's a pity we didn't get a result in the end."