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."
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