matches remaining.Moyes was barracked by the home support throughout and one Everton fan even turned up in a Grim Reaper's costume to poke fun at the United boss from just behind the dugout.
On the pitch it was a grim day for the United boss as his team suffered their 11th defeat of the season.
Phil Jones blocked Romelu Lukaku's shot with his outstretched arm and Leighton Baines converted the resulting spot-kick before Alex Buttner played Kevin Mirallas onside and the Belgian beat David de Gea from a tight angle.
Moyes tried to put a positive spin on what was a dreadful defeat, but he did not hold back when giving his assessment of his team's defending for both goals.
"I thought the two goals we conceded today were rank, rotten," the United boss said.
"The (first) goal was a big kick up the pitch, it was nodded down and picked up, and for us to concede a goal like that was terrible.
"The second was a better move but we should have defended it much better that we did.
"We gave away two terrible goals but prior to that we passed the ball brilliantly well, kept the ball, had great control of the game.
"What we couldn't do is make enough chances, but we had a great control and we got done by two stupid decisions."
The result and the performances of both sides showed just how much United have regressed under Moyes and how far Everton have come under his successor Roberto Martinez, who has now collected a record 20 league wins since moving to Goodison Park.
United tested Tim Howard on just two occasions while Everton out-muscled and outclassed their opponents in midfield.
Wayne Rooney had a disappointing afternoon in front of goal while Lukaku caused Jonny Evans and Jones problems throughout.
Moyes, surprisingly, thought his team did not play too badly.
"We played very well in the first half," said Moyes, who spent 11 years at Everton before moving to Old Trafford.
"We had passed the ball really well, kept the ball but we didn't have the final pass, the killer through ball that was needed in the final third.
"I didn't think we deserved to go in 2-0 down at half-time, that's for sure.
"We had good play, good control of the game, and we had the bulk of the ball."
Martinez, who became the first Everton boss to do the double over United in 44 years, hailed his team's performance as "electrifying".
"This was an important win for our fans," said the Spaniard.
"We knew that since the 1969-70 season we had never done the double over United and I think that is when we won the league.
"That tells you this group of players is ready to develop.
"That performance was full of energy, it was dynamic on the counter attack
I thought we looked electrifying."
Despite the midweek defeat to Crystal Palace, Everton are just one point short of fourth-placed Arsenal with three matches left.
Martinez is refusing to get carried away with talk of his team pipping the Gunners to fourth, though.
"We have another nine points to fight for," said Martinez.
"We play Manchester City, Southampton, and Hull a week before the cup final
You couldn't pick a worse three games."
For Moyes the season is over
He now has the unwanted tag of being the man who has failed to take United into the Champions League for the first time in 19 years.
As ever, there was an attempt from the Scot to cast a positive light on his team's woeful season.
"I think everybody knows that we are on track to make changes and do some different things," he said
"We are rebuilding
"I understand it has not been good, I recognise it has not been good, and it needs to be better."
Source : PA
Source: PA