Juan Pablo Angel equalised for Villa from the penalty spot in the last seconds of four minutes added time to turn the jeers of the home fans into cheers.
Villa looked unlikely to score despite the greater share of possession in the second half yet Gregory insisted: "We deserved to win the game, let alone draw it, given the amount of possession we had.
"We have been on the receiving end of last-minute goals against West Ham and Arsenal recently and we had a break ourselves today.
"The guys kept grinding away. We've not had the results we've wanted in the last few weeks and to have gone down 1-0 would have left a bit of a cloud hanging over Villa Park.
"But we showed a lot of guts, pinned Tottenham back in their own box for the second 45 minutes but could not turn the pressure into goals."
Aston Villa manager John Gregory claimed his side deserved more than a point after Saturday's 1-1 draw.