The Blues, who ended the game with 10 men following Ashley Cole's late sending off, dominated the second half, but looked set to leave south Wales empty handed thanks to Scott Sinclair's superb first-half volley against his former club but Jose Bosingwa's stoppage-time cross deflected in off Neil Taylor.
"I think it was a very different first half to the second, completely different. In the second half we were more confident and caused Swansea a lot of problems by pressing high," said Villas-Boas.
"The first half was the opposite, we conceded territory and they found spaces and caused problems. Their goal came during the period when we were starting to do things right, we had plenty of the ball but didn't take our chances.
"The second half was very good, a big effort to improve things, if the goal had come earlier we could have got the second due to the motivation and momentum, but they defended very well.
"The goal was a reward for what the team was doing, but we are unsatisfied because if we had played like this in the first half we would have won the game. We let Swansea have that advantage but we responded in the second 45 minutes."
Cole's sending off, after he picked up a second booking for a sliding challenge on Nathan Dyer, means the England full-back will miss this weekend's crunch clash with Manchester United.
And Villas-Boas admits the loss is a big blow to the Blues, who were without John Terry due to a knee injury, with the England captain's court case into his alleged racial abuse of Anton Ferdinand - which he strenuously denies - set to begin on Wednesday.
"His first booking was fair, the second was a more difficult challenge to asses due to the speed it happened at. Ashley thought he was getting the ball and Dyer anticipated but I am not sure there was enough contact (for it to be a booking) as Dyer got up straight away.
"He is one of our key players, Ashley is immense and of course he will be a big loss."
Source: PA
Source: PA