Ole Gunnar Solskjaer’s team capitulated at Goodison Park as they failed to take advantage of other teams’ slip-ups as they chase down a top-four place in the Premier League.
United looked beaten by half-time after goals from Richarlison and Gylfi Sigurdsson put Everton two up at the break, before Lucas Digne and Theo Walcott followed up in the second half to condemn the visitors to a sorry defeat.
And afterwards, Matic said that it was the responsibility of the team’s more experienced members to shoulder the blame for the collapse.
“It's one of the worst games for me personally, and for the team,” said the Serbian.
“I think we deserved to lose. We did not play how we wanted to play.
“It's hard for me to speak about. It’s not for the young players. I’m one of the most senior players. If anyone is to blame for this it’s me.
“When you win the battle in midfield it's easier to play. We didn’t do that today.”
Everton collectively outran United by 8 kilometres at Goodison Park, on a day when the visitors saw their goals-against tally tick over to 48 in the league.
That set a Premier League record for the 20-time champions, who have now conceded more goals than they did in what was previously their most porous season.
The team let in 45 goals in 1999/00 and 2001/02, but this season’s record looks set to cost them a place in the top four and consequently next season’s Champions League.
“It’s shameful,” said Matic. “We have to look for the mirror, everyone has to see where he made mistake and what he must do better.
“The more guilty are the more experienced players and in this case it’s me.
“It’s difficult to answer what is wrong. Our approach to the game was not good, everyone needs to take responsibility during the game, with the ball, without the ball, everyone needs to run more then our quality will show. “