Big-name former United stars Roy Keane and Peter Schmeichel have both condemned some members of Moyes' under-performing squad in recent days.
On Tuesday, Keane singled out Ashley Young and Rio Ferdinand for treatment, whilst Schmeichel has claimed some Red Devils players "look as though they don't care".
It goes to the heart of a problem that, unless it is resolved, will continue to undermine Moyes' hopes of a successful transition from the Sir Alex Ferguson era.
"This squad was good enough to win the league last year," said Moyes.
"I need to make sure we get them back playing at that level again.
"I take responsibility. I always do. It is the manager's job.
"I will try and make sure that from now on there are no questions about their application."
Given there have already been concerns expressed around the United dressing room about a lack of fight, it is unlikely Moyes is unaware of the issues Keane and Schmeichel have raised.
Indeed, privately, it would be no surprise if he agreed with at least some of them, with Schmeichel's status as a club ambassador giving even more weight to his comments.
Certainly it appears the clock is ticking on a few high-profile United careers, with Moyes admitting, ahead of Sunday's Premier League trip to Aston Villa, that changes are going to be made.
"We are making sure everyone has an opportunity to show the new manager exactly what they can do," he said.
"We are trying to be as fair as we can to the players who are here.
"We have really good players. These are near enough all the players who were involved last year. Hopefully we can get them in top form.
"I have a good squad. Can I improve it? Of course I can. Am I going to improve it? Yes I am.
"Undoubtedly we will alter things in the coming months and transfer windows. Will they come in January? I don't know."
Yet Keane has not just been critical of United's players this week.
In his ITV4 documentary with Patrick Vieira, the Irishman also reignited his feud with Sir Alex Ferguson by claiming the Scot was still exerting his influence at Old Trafford, which was perceived as undermining Moyes.
It is true Ferguson has been fairly visual in recent times, travelling to Bayer Leverkusen recently, his first European away game since standing down in the summer.
But Moyes does not view his presence as a distraction.
"I can only tell you that in my time here Sir Alex has been fantastic towards me," said Moyes.
"He has been helpful.
"Anytime I need something I can go to him. He has been very good."