Gylfi Sigurdsson gave Tottenham the lead in the 19th minute and they should have doubled the advantage just before the break, but Paulinho could only hit the post after good work down the right by Andros Townsend.
Chelsea levelled through John Terry 20 minutes into the second half and the visitors looked the more likely to claim a win, but Fernando Torres was sent off for a second booking nine minutes from time as it ended all square.
Villas-Boas felt his side had deserved better for a strong first-half performance and lamented their failure to kill off the game.
He said: "I think the (key) moment of the game was when Paulinho hit the post just before half-time. Had that gone in it would have put us in a very good position. I think we deserved that for the first half that we played.
"The second half was not well played by either team, but I think Chelsea had the upper hand and were more dangerous on the counter-attacks. They deserved to get the equaliser."
Chelsea boss Mourinho was left angered by Torres’ red card - with both bookings for fouls on Jan Vertonghen - but Villas-Boas felt that the decision was justified.
He added: "I think regarding the second incident, it is difficult for the referee to judge. They both went for the ball and the referee decides to caution Torres.
"Perhaps that one was a little dubious and unfair, but I think there were some incidents before which could have got him the red card earlier.
"Jose will be annoyed with the sending off."
Villas-Boas also spoke about his relationship with former colleague Mourinho, with much of the build-up to the match having been dominated by suggestions of a falling out between the pair.
However, the Tottenham boss preferred to focus on the match.
He said: "We had a brief chat. I have explained that I would invite him (for a talk), but I have to leave. I think the attention should not be drawn on managers, but on the match.
"It was a hard-fought battle. Two teams that wanted to win. It was a fair result, but the league will not be decided in matches like this."
