Moyes has endured a difficult first season at Old Trafford since being charged with the task of replacing the legendary Alex Ferguson and this week wrote to season-ticket holders to thank them for their support.
United are seventh in the Premier League ahead of Saturday's trip to West Brom and face a battle to stay in the UEFA Champions League after losing 2-0 at Olympiacos in the first leg of their last 16 tie.
It has been suggested that Moyes' players are not playing for the Scotsman, but the United boss rejected that notion.
He said: "I don't know if it's the right thing (to state) that they're not playing for me. 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. I've done it with the supporters.
"We need to play better. I think Olympiacos 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."
Former Netherlands international Ronald de Boer this week claimed that Van Persie may leave Old Trafford if United fail to strengthen their squad at the end of the season, but Moyes played down such claims.
"I couldn't reply to that and I wouldn't know how Ronald de Boer would know that," added Moyes.
"I travelled back from the (Netherlands) game (a 2-0 defeat against France on Wednesday) 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."
