Midfielder Matic was at fault for Everton's second goal when he allowed Gylfi Sigurdsson the space to score from 20 yards, and the Serbia international admitted he could have done better.
"Many things didn't work for us today," he told TV2. "First of all, our approach.
"I think that the most experienced guys, in this case me, didn't play well today. So I don't think we need to blame the young guys today. I was the biggest problem.
"In these kinds of games, you have to win the battle in the middle, then the team can play better football. We didn't do that."
United remain in the hunt for a place in the top four after both Tottenham and Arsenal lost over the weekend.
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They face Manchester City at Old Trafford on Wednesday, and Matic said the players had talked about how to put things right.
"We had one small meeting," Matic said. "We will try to do better in the next few days. We have a big game against Manchester City, so we will see if we're ready.
"We'll keep it behind the doors, but I think it was a good meeting."
United manager Ole Gunnar Solskjaer questioned his players' desire and commitment after the match, while pundit Gary Neville said some of them had been "embarrassing."
Ashley Young, who came on as a half-time substitute, urged his teammates to hit back against City.
"We know how important that's going to be," Young told MUTV. "If you can't get yourselves up for the Manchester derby, there's something wrong.
"I've got confidence that we're going to be ready for Wednesday. We've got to dust ourselves down fairly quickly and go again this week."