Ole Gunnar Solskjaer's United have lost six of their past eight matches and Matic was candid in his assessment of the Goodison Park rout post-match.
"The biggest problem was that we didn't have leaders on the pitch," Matic, 30, told Stadium Astro.
"In this case me, because I'm one of the most experienced guys in the team so if we don't win that battle in the middle, for our team it is difficult to play.
"If someone is to be blamed for this game it is me.
"I think that I'm most responsible because I'm one of the most experienced guys in the changing room."
Their crosstown rivals currently sit two points behind Liverpool as Man City look to chase down another Premier League title.
United, meanwhile, have matches against Chelsea, Huddersfield and Cardiff to wrap up the Premier League season as they push for a spot in the Champions League next season, which will be Solskjaer's first full campaign in charge of the club.