The Hammers have appealed against the 15th-minute dismissal, which came after Feghouli and Phil Jones both lunged into a 50-50 challenge.
It was the fifth Premier League red card Dean has shown this season and his 25th since the start of the 2013-14 season, in both cases the highest tally in the league.
He was widely criticised by pundits and former referees — including Mark Halsey, who believed Dean was influenced by his failure to dismiss Everton’s Ross Barkley in December 19’s Merseyside derby.
Halsey said: “Initially I thought it was actually Phil Jones who was going to be sent off.
“Mike looks away and then looks back and sees Jones on the ground in agony.
“Perhaps he felt disappointed that he missed Ross Barkley’s shocking tackle on Jordan Henderson only a couple of weeks ago and he has guessed because of what happened at Goodison Park.”
Another ex-Premier League referee, Dermot Gallagher, added: “He’s taken his time, but he’ll look at it today and say he got it wrong.
“He’s the most experienced referee in the Premier League and I think he’s made less errors than any other referee. Because Mike Dean doesn’t make errors, that’s what’s made it so focal.”
During Monday’s match, Sky pundit Niall Quinn labelled Dean “arrogant” and the decision “rank bad refereeing”, while his colleague Alan Smith felt Dean “wants to be the centre of attention”.
While Gallagher feels the error is uncharacteristic, the dismissal is certainly not.
Over those three-and-a-half seasons, Dean has produced his red card 25 times in 103 games, or once every 4.12 matches — over 50% more often than the Premier League average of one every 6.25 games.
The other referee to have come under focus for a red card on Monday, Lee Mason, is slightly above average at one dismissal every 5.86 games.
Mason sent off Manchester City’s Fernandinho against Burnley, with City full-back Bacary Sagna claiming afterwards on Instagram that the match had been “10 against 12” — though Gallagher insisted the Lancashire official had “no alternative”.
The now-retired Chris Foy is closest behind Dean with one red card every 4.2 games (10 in 42), with Phil Dowd and Jon Moss the only other officials to dismiss a player more often than once every five games.
Dean is a near-constant presence at the top of the major refereeing statistics, having also given penalties most often over the same period of time.
The 35 he has awarded have come more often than one every three games, a mark otherwise only reached by Bobby Madley (20 in 59), with the pair comfortably clear of the pack.
Dean is second in yellow cards with 3.85 per game — albeit a long way behind Phil Dowd’s league-high average of 4.50.
However, when it comes to fouls given, Dean’s average of 21.4 per game is almost exactly in line with the league average and only eighth out of the 18 referees who have taken charge of at least 20 games in the time period.