United enjoyed long spells of possession at Goodison Park but struggled to create any real openings as Everton ran out 3-0 winners thanks to goal from James McCarthy, John Stones and Kevin Mirallas.
The game followed a similar patter to United’s defeat to Chelsea last week and Carragher thinks Roberto Martinez paid close attention to Jose Mourinho’s tactics to help steer his side to victory.
“We’ve been very complimentary about Manchester United in the last few weeks,” Carragher, speaking on Super Sunday, said.
“Louis van Gaal has got a system, a way of playing but in the last week it looks like teams have come up with a way of playing against them. They are saying: have the ball.
“This is Roberto Martinez. Jose Mourinho is that type of manager but with Roberto Martinez, his teams would never normally have such low possession.
“But against United, they accepted they’ll have the ball and decided to hit them on the counter-attack.”
Carragher was full of praise for Everton’s midfield trio of McCarthy, Gareth Barry and Ross Barkley and insists they were the key reason behind the Toffees’ third consecutive home win against United.
He added: “In the midfield areas, there was a job that was done last week by Zouma on Fellaini. I think Gareth Barry did a similar job today but the fact James McCarthy got the man of the match and Barry was in the running was the job they did.
“It wasn’t just Fellaini in this midfield for United; it’s the job of Herrera as well. McCarthy looked after him, as did Ross Barkley. You wouldn’t say he had his greatest game in terms of being on the ball and going forward but how disciplined he was. His job was to stop Daley Blind.
“Those three players were virtually doing man-marking jobs and the three of them did it excellently. That’s where they got the win from because they won the ball back quickly and could counter-attack.
“It looks like teams are looking at Manchester United and thinking how to stop them. Chelsea and Everton have come up with a way, certainly in those midfield areas.”
Speaking on his podcast, Gary Neville was also critical of his former side, labeling them “toothless” in defeat.
“It was a strange game, and you would have thought that both teams had nothing to play for in some ways,” Neville said.
“The atmosphere was strange all day long. Usually when Everton are beating Manchester United the place would be bouncing.
“United were toothless, and that is being kind.
“I didn’t really see them try and dribble past a player, make any forward runs.
“At times they were not getting enough men in the box and the final pass was poor.
“It is the worst I have seen United play for five or six weeks.
“They have been playing so well. Even in defeat at Stamford Bridge last week they played really well.
“Today it wasn’t there. It was Everton who had the cutting edge. It was through Lennon, Lukaku and Mirallas when he came on who looked the ones most dangerous to break through either defence.
“For a long time United have had a good record at Everton but certainly not in the last three seasons.
“Last season was such a poor performance. I don’t think United were that bad today, despite it being a worse result.
“Today United just didn’t come to terms with how they had to play the game. They needed to show more urgency.”
United looked vulnerable through the middle at Goodison without the injured Michael Carrick to protect the back four.
The influence of the England midfielder cannot be underestimated. United have won 72.2 per cent of the matches that Carrick has started but just 37.5 per cent of encounters without him in the team, and Neville feels United are a different side without the veteran.
“When Michael Carrick doesn’t play, their record without him shows he is missed,” Neville added.
“It is not just the control and composure, but it is his forward passes, he just moves the ball forward into good areas quickly.
“When United won the ball back today they didn’t get the ball forward quick enough.
“Michael Carrick does that. Even if it is only a 10-yard pass, he gets the move moving in the right way.
“They miss him badly, they really do. It is no coincidence they have lost the last two games without him.”