The visitors were leading 1-0 courtesy of a Robin van Persie header, his 18th Barclays Premier League goal of the season, when substitute Wayne Rooney went down under a challenge from Steven Caulker inside the box.
Referee Chris Foy declined to award a penalty and Spurs, who dominated the second half, eventually scored a dramatic equaliser through Clint Dempsey two minutes into stoppage time.
Villas-Boas was unsure whether Caulker had caught Rooney but did not want the argument to overshadow his side's efforts.
He said: "Obviously it is going to be debated and debated and I hope it doesn't mar the game.
"During the game we got most of the decisions against us. I prefer to look at this game on my view and United prefer to look at it on their view.
"We take our boost of confidence and the debate is going to be whether it was a penalty because that is controversy and it sells better but we shouldn't mar the game and the quality of the game played in these difficult conditions.
"Fortunately we got a point, I think it is credit for the game that we had. We were the best team and created the best chances.
"I think it was probably the worst United game in terms of opportunities, with them having only four. It is a pity we couldn't win but I'm extremely happy with the draw obviously."
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