The referee, who will be in charge of next month's FA Cup final between Chelsea and Everton, is widely considered to be the country's top official but has been heavily criticised following the controversial incident.
United were trailing 2-0 when Webb ruled that goalkeeper Heurelho Gomes brought down Michael Carrick even though replays clearly showed the Spurs man touched the ball first.
Enlarge Fingers of fate: Gomes gets a hand on the ball and can't believe when a penalty is given against him (below) at Old Trafford
Cristiano Ronaldo converted from the spot and United went on to record a comfortable 5-2 win. Speaking after the game, Tottenham manager Harry Redknapp claimed that the decision cost Tottenham the game, while midfielder Jermaine Jenas accused Webb of 'crumbling' under pressure at the home of the champions.
And now former Premier League referee Dermot Gallagher has revealed that Webb spoke to him about the incident and admitted he had got it wrong.
Centre of a storm: Howard Webb waves away Spurs' protests
'I talked to Howard and he knows he made a mistake,' Gallagher revealed. 'He didn't think the goalkeeper had got the ball. He thought that Carrick had touched the ball sideways and then the goalkeeper brought him down.
'I don't think it was an easy decision, as people say it was, but it's clear to anyone that it was a mistake.
'But these things can happen to anyone and I think it's important we move on from it. Anyone could have fallen foul of making a mistake like that, we've all done it.'
Gallagher, an experienced official who now acts as a TV pundit as well the referee on ITV Sunday evening fare Beat the Star, insisted Webb should not be sanctioned for the blunder.
'Punishing him won't do him any good and it won't do the clubs any good either, because the game is over now,' he said.
'He won't lose the FA Cup Final. It was one decision in his career and you have to accept that people make mistakes.'
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