Spurs arrived at the Etihad Stadium looking to claim a Manchester double, having already taken three points off United at Old Trafford this season.
In an effort to secure such a success, Villas-Boas preferred former City striker Emmanuel Adebayor in his starting XI over the in-form Jermain Defoe.
Everything was going to plan at the interval, with Steven Caulker nodding Spurs in front, but Sergio Aguero and Edin Dzeko hit back for the hosts to snatch the spoils.
Villas-Boas believes Adebayor was the right choice up front, as he offered a physical threat against City's back four, but is disappointed to have ended the game empty-handed.
"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.
"In the end, he (Adebayor) had a positive impact regarding the structure we put together. It's a pity we didn't get a result in the end."