Spurs are still awaiting their first win under the 34-year-old, with a point against West Brom and a defeat at Newcastle, in addition to Saturday’s stalemate, amounting to the Portuguese's achievements so far in north London.
And Villas-Boas, appearing calm post-match, added that it was “normal” for a team to start slowly under new management.
"I think it's normal [to wait for first win]. It comes normally with hard work and we continued to work hard today," he added. "I think the first half we weren't so sharp, like last week we didn't create lots of opportunities, so today was a little bit different.
"Second half we improved a lot, managed to have more of the ball and were creative. We fought hard to get the goal that we deserved but in the end suffered again on a set play.
"I think it's obviously disappointing start for everybody, but we look to repay our fans with the win they deserve and the team deserve, we will continue to pursue that."
The Portuguese also confirmed that despite splashing out 15 million pounds on a new goalkeeper on Friday that veteran Brad Friedel would continue to be his first choice.
The France captain moved to White Hart Lane on Friday and was expected to replace the American, but the Portuguese coach confirmed the 41-year-old will keep his place after a fine showing in Spurs' 1-1 draw with Norwich on Saturday.
He added: "[Friedel] had an amazing game, you have to give credit to him. It was a man of the match performance, he saved us a couple of times from going 1-0 down, it was so outstanding.
"Obviously competition increases for him, but the place is his because he is a tremendous goalkeeper and deserves that spot."