The visitors were leading 2-0 when Webb ruled that Spurs goalkeeper Heurelho Gomes had fouled Michael Carrick after 57 minutes when television replays showed he had palmed the ball away to safety before colliding with the midfielder.
Cristiano Ronaldo converted the penalty and put United back into the game, which they went on to win 5-2 to return to the top of the table.
Webb told the BBC: "I've looked at it again and I think it was a mistake but we make these decisions honestly.
"It's not always easy to see the way the play pans out from pitch level."
Speaking to BBC Radio Cambridgeshire, Webb added: "I could see the Manchester United player touch the ball and saw him get clattered by the goalkeeper but didn't see the extra deviation from the goalkeeper's fingers touching the ball.
"I'm disappointed as I always strive for perfection. I'll look at the tape in detail later in the week and try to avoid it happening again in the future.
"I never want to have a negative impact on a game and I get no pleasure from not reaching the high standards we set ourselves."
Spurs midfielder Jermaine Jenas criticised the decision saying that Webb "crumbled under pressure" and the player could now face disciplinary action from the Football Association over his comments.
The FA has given him seven days to explain his remarks after he was quoted as saying: "The atmosphere, the occasion, the importance of the match, a lot of factors take their toll when making decisions.
"One thing which struck me was that he didn't even think. It was like he'd already made his mind up when he came out for the second half that he was going to give something.
"I think it was a case of the referee crumbling under the pressure at Old Trafford really."
Webb will officiate at the Reading versus Birmingham City match on Sunday in the season's final round of Championship games. Both teams have a chance of earning automatic promotion to the Premier League.
NEWS: Gallagher - Webb admits to making penalty mistake
NEWS: Jenas: Webb wilted under Old Trafford pressure
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