After 26 years at the helm, Sir Alex Ferguson stepped down as United boss at the end of last season.
The Scot won 38 trophies during a long, illustrious reign, including last season's Barclays Premier League crown.
Everton boss Moyes was the man chosen to fill the void, but he has yet to set the world alight with the Red Devils.
Next up is a Premier League clash with Crystal Palace, whose manager Holloway believes Moyes can be a success with United.
"It is the end of a legend," Holloway said. "Ferguson has left a legacy behind him.
"But David is a fantastic manager and he has decided that is what he wanted to do.
"It was an honour for him to get the job and good luck to him, but not this weekend.
"Only time will tell for all of us what we leave, the mark we leave at each club that we work for.
"I hope Dave leaves a fantastic mark on Manchester United. He has worked so hard, he deserves it and good luck to him, but I am more concerned about my team."
After winning the Community Shield against Wigan, Moyes' side beat Swansea, then drew with Chelsea before losing at Liverpool.
It means United are just a point better off than newly-promoted Palace heading into the match, but Holloway does not read too much into that.
"I think it is an honour going to Man United, whatever time it is, whoever the manager is, whoever is in charge," he said.
"At this moment in time they are in a transitional period.
"They've got a new manager, who was chosen by the last one - you don't get much better on your resume than that. To hear 'I want him to replace me' must be an honour.
"But the fact of the matter is David has to make his mark on Manchester United - I've got to make my mark on Crystal Palace.
"Is it a good time to play them? I will tell you after the game.
"The fact of the matter is he has not had long enough to be judged yet. I don't feel I have and I have been here six or seven months.
"I've just bought some of the players I've wanted to bring and added to the group I inherited. Hopefully the group will grow and try to improve on what we do.
"Two or three years ago Crystal Palace beat Man United 2-1 at Old Trafford. I can remember watching that on TV.
"That was in a cup competition, now we're in a league against them, which is fantastic for us. Let's see if we can do that again."