The Chelsea boss on Monday takes his team to Old Trafford, seeking to strike the first blow in the Premier League title race.
Moyes is seeking to defend the Premier League title Sir Alex Ferguson won before retiring as United boss.
Mourinho does not think it is possible to compare Moyes with his predecessor, yet.
"One has an incredible history there and another one has just arrived," Mourinho said.
"Is that a problem for David? I don't think it is. He's an experienced manager, he has had years and years and years in the Premier League.
"He works at this moment with better players than he did in the past (at Everton).
"In this moment he has different ambitions than he had in previous years.
"Now he knows to be successful, he has to win trophies with Man United."
Moyes' measure of achievement will be different now he is at a different club.
"It's difficult to win it (the Premier League) with Chelsea, it's more difficult to win it with Everton," said Mourinho, who won the title twice, in 2005 and 2006, and is now in his second spell at Stamford Bridge.
"He did his job very well with Everton, that's why he's at Man United.
"You have to measure success by the ambitions of the club where you are.
"If (Ian) Holloway keeps Crystal Palace in the Premier League, after bringing Palace to the Premier League again, I think it's a huge success. But he doesn't win the Premier League.
"You have to measure success in relation to the potential of the teams. And David was successful in Everton."
Wayne Rooney is sure to be the centre of attention at Old Trafford, given Chelsea's pursuit of the striker and Mourinho's stated intent to make a third bid following the match.
As far as the title race goes, Mourinho has tried to downplay the significance of the clash, even though victory would take his side six points clear of United, albeit with a game in hand.
"Every game has an influence," said Mourinho, whose side began the season beating Hull 2-0 and Aston Villa 2-1.
"If we lose against Aston Villa, if we lose two points, I think it can affect (the title race).
"I know this is not a two-horse race, because in the championships where it is a two-horse race, the two big matches are much more crucial.
"In this case, it's not like that. In between six teams we have to play 10 big matches.
"It's different, but it's a match where every point we get is one point less than the opponent gets. It's important, but it's the beginning of the season."
Mourinho knows taking on Manchester United is never a straightforward task, although he opted against comparing the current squad with past ones.
"(It is) always tough - some of the best players in the world, some of the best players in this country," Mourinho said.
"Always a mixture of young talent with the players that carry the flag of Man United history. It was like that in my time.
"In my time they had Roy Keane, (Paul) Scholes, players with big history there.
"Now they have still players from my time. Like (Rio) Ferdinand, (Nemanja) Vidic, (Ryan) Giggs and they have this always mixed with very good young players.
"With that winning culture that makes the basis of big clubs. And they are a big club for many, many years. They have everything."