United were comfortably beaten by Marco Silva’s side at Goodison Park and fell to a sixth defeat in eight games in the process.
Matic was returning from a spell out of the side due to an illness and often found himself bypassed in central midfield.
The 30-year-old was largely to blame for Everton’s second goal, having failed to close down Gylfi Sigurddson and allowed a shot from range.
Speaking to Norwegian television channel TV2, Matic acknowledged he played poorly and said as a senior member of the United squad, he was to blame.
“Several things didn’t work for us today. First of all our start to the match,” he said, referencing Richarlison’s 13th-minute opening goal.
“I, the most experienced of all of us, did not play well today. We can’t blame the young players, I was the biggest problem for the team today.
“In such matches you have to win the duels in the middle, so the team can play better. We didn’t do that today.”
Thanks to Arsenal’s surprise home defeat to Crystal Palace, United remain only two points away from the top four with four game remaining.
United welcome champions Manchester City to Old Trafford on Wednesday night, with fifth-place Chelsea visiting next Sunday.