The Spurs were leading 2-0 when Webb ruled that 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 United went on to win 5-2 to return to the top of the table.
Webb told the BBC: "I think it was a mistake but we make these decisions honestly. I'm disappointed as I always strive for perfection. 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."