Jermain Defoe looked to have secured a point for the visitors when he cancelled out Olof Mellberg's opener but Martin Laursen popped up with five minutes remaining to maintain Villa's fine form over the festive period.
They have now claimed eight points from their four games and are well poised to make a push for a Champions League spot.
"I was worried before the game because Tottenham have been in fantastic form," O'Neill told Sky Sports 1.
"I was concerned about our energy because of the big efforts in games we've played recently.
"I thought our energy might drop a little but we showed fantastic desire.
"No-one epitomised that more than Laursen. He was incredible tonight."
Mellberg feels his side's form over Christmas will be crucial to how they perform in the second half of the campaign.
"It's a very important victory," he said. "We were talking about the period at Christmas and last season we didn't do that well and we struggled after that.
"These games are massive, especially Tottenham. It's a big win and to get a win at home is important."