David Moyes has strongly denied any suggestion Manchester United's players are collectively unhappy with his management and insisted Robin van Persie is settled at the club despite Ronald de Boer's claims that his fellow Dutchman might want to leave.

Moyes, whose team visit West Brom in Saturday's lunchtime kick-off at the start of a critical three-week period, said he plans to begin easing Nemanja Vidic out of the team after confirmation from Internazionale that United's captain will be moving to San Siro next season, a statement that has caused disquiet at Old Trafford because of its timing.

However, the United manager made it clear he does not expect Van Persie to follow Vidic out of the club despite De Boer saying this week that the striker was "not enjoying the football Manchester United play" and contemplating his future.

"I couldn't reply to that and I wouldn't know how Ronald de Boer would know that," Moyes said. "I travelled back from the [Holland] game with Robin the other night. I went to the game, watched them play and travelled back with him. I hardly feel I need to answer the question."

Moyes went on to say he had no issues with Van Persie's comments about the team's tactics after the 2-0 defeat to Olympiakos – "none whatsoever, if you actually read the full transcript I understand totally where he was coming from" – and added there was no issue between Van Persie and Wayne Rooney. Statistics in recent weeks have shown a sharp deterioration in their link-up play, most notably against Olympiakos when Van Persie played one pass to Rooney, direct from the kick-off.

"The statistics before they both came back [from injury] proved that we had lost one game with them in the team up until the previous three or four games," Moyes said. "The record with the two of them in the team was fantastic, so I was talking up how good they were together a month ago. It's only in the last couple of games that has gone. We didn't play well at Olympiakos but prior to that we won at Palace and drew at Arsenal. It was that one game that has dragged this up."

United, seventh in the Premier League and 18 points behind Chelsea at the top, lost to West Brom at Old Trafford earlier in the season and desperately need a better result this time bearing in mind they face Liverpool and Manchester City before the end of the month.

"I don't know if it's the right thing [to say] that they're not playing for me," Moyes said. "I think they definitely do, so I don't accept that. I've been honest with the players and the media, I've tried to be straight as I can. We need to play better. Olympiakos was the poorest we've played. That was disappointing but we will improve from that and we will be better.

"We had a bad night and we all take responsibility for that. But I refute that was the worst night or all those sort of things. We didn't play well, we said that honestly and we know we have to do much better. The players are aware of that and we will have to do better in the coming months."

Vidic will continue with the captaincy but Moyes intends to use him more sparingly now his move to Italy is confirmed. "Undoubtedly I am going to try to give the younger centre-halves opportunities to show what they are capable of. Going into this period of the season we will look to see how Chris Smalling, Phil Jones and Jonny Evans, when fit, are able to handle this part."

Asked about the announcement from Inter, Moyes said: "I don't think we like it in this country. I don't think it's something that's done here. I can think of [Robert] Lewandowski going to Bayern Munich. I can think of [Mario] Götze, who went last year between two of the biggest clubs in Germany. It's not something we like in this country, it's done more often elsewhere. But it's happened and we'll get on with it. Vida has been a brilliant servant for the club and we'll treat him with all the respect he deserves. I knew about January time that this would probably be his choice."

Moyes has put together an open letter for United's season-ticket holders thanking them for their support – "The difficult season we have experienced was not something that I envisaged," he writes – but admitted at Friday's press conference it was an idea from elsewhere within the club.

"I was asked to put out something to the supporters to say: 'Here we are, this is how it's gone about' but I think most Manchester United supporters totally understand the situation. They've shown that with their backing wherever I've been, not just at Old Trafford but everywhere. I've been to a lot of games all over the world and all the Manchester United supporters I bump into understand we're having a difficult season and they're looking forward to it getting better."

Moyes also showed his disdain for the coverage of the online petition demanding Tom Cleverley does not play for England. "I am surprised that the media would be picking something up on social media and making a big case out of it because that is wrong."