McTominay said that the atmosphere in the dressing room has been "toxic" under former managers but says it has not reached that stage under Ten Hag.
United are plotting an unlikely path into the round of 16 of the Champions League, needing to beat Bayern at Old Trafford on Tuesday and hope FC Copenhagen and Galatasaray draw in the other game in Group A.
"It is the players' responsibility, first and foremost," McTominay told a news conference on Monday.
"The players know that as well. We have had many amazing players and right now we are at the stage where we have big characters in the dressing room.
"It is not just a case like some of the other managers where it has been a little bit toxic at times, the boys are firmly behind the manager.
"I have said that in many other interviews and that is the way it will stay. We have got an amazing coaching staff as well so it can get lost in translation with what the players think and what is said behind closed doors, we just want to do well for the football club."
Saturday's defeat to Bournemouth was United's 11th in just 23 games this season as Ten Hag's team has struggled to build on the positivity of the Dutchman's first campaign in charge.
They have already lost six home games this season and need to inflict Bayern's first Champions League group stage defeat since 2017 to have any hope of continuing in the competition.
"What I know is I never think of a negative scenario," Ten Hag said.
"We think positively. We know what to do, we have to win to stay in Europe, it's about that. We will prepare the team with that feeling, with that belief, we have shown in the last weeks when we are at our best we can do it."
"We have to show them [the players] the clips from Chelsea," Ten Hag said.
"How they can play, if we do that, all there, and we have a good plan and, as I said, we can beat any opponent.
"I think Old Trafford is not a nice place to come for an opponent. We are aware of it and it starts with us. We are together and as long as I am here I have the feeling we are absolutely together."