Webb found himself at the centre of mass controversy at the weekend after penalising Spurs glove-man Heurelho Gomes for an alleged foul on Michael Carrick.
Cristiano Ronaldo despatched the spot-kick, allowing Sir Alex Ferguson's side to come from 2-0 down to triumph 5-2 and remain firmly on course for a third consecutive Premier League crown.
Television replays clearly showed Gomes won the ball inside the danger-zone, with the dubious decision slammed after the match by both Tottenham manager Harry Redknapp and midfielder Jermaine Jenas.
However, former referee Gallagher has revealed that Webb has admitted he got the decision wrong.
"I talked to Howard and he knows he made a mistake," he said.
"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. Punishing him won't do him any good and it won't do the clubs any good either, because the game is over now.
"Of course he won't lose the FA Cup final. It was one decision in his career and you have to accept that people make mistakes."
NEWS: Jenas: Webb wilted under Old Trafford pressure
NEWS: Redknapp rages at Webb spot-kick shambles
SPURS FANS! Check FourFourTwo.com’s ever-expandinginterviews archivefor more stuff to read:
Web Exclusives Les Ferdinand, Paul Gascoigne, Gary Lineker, Glenn Hoddle, Frederic Kanoute
One on One Paul Gascoigne, Les Ferdinand, Ossie Ardiles
Boy's A Bit Special Chris Gunter, John Bostock
Ask A Silly Question Garth Crooks
Perfect XI Ossie Ardiles
My Secret Vice Neil Ruddock
Plus! Martin Peters on Weekend Wonders and Spurs on Talentspotter
