There was no hint of antagonism towards his rival when Mourinho assessed the job ahead of Moyes, despite the fact the Portuguese is trying to lure Wayne Rooney to Stamford Bridge from Old Trafford against the new United boss's wishes.
"One of the most difficult things in the club is to create a victory culture, where you walk through the door and you smell the success, you smell confidence, you smell self-esteem," Mourinho said.
"David is in a big club and that is a big help - everybody knows how to win. Of course, it is up to him now. He has to coach, he has to decide who to buy, who to play, he has to train them every day, but a big club with a big winning culture is there.
"If I was in Spain at this moment I would wish him very well because he deserves good things, (but) I cannot wish him very well because he is competing against me."
In 10 years at Everton Moyes did not win a trophy, but Mourinho dismissed that statistic as irrelevant.
The 50-year-old said: "When he finished fourth with Everton or fifth, it's a trophy. I hope he gets some with Man United. Not many because we want some for us."
Ferguson signed off with the Barclays Premier League title Moyes is trying to retain under pressure from Mourinho, who, alongside Arsene Wenger at Arsenal, is now one of the senior management figures in the top flight.
Mourinho feels a responsibility to help fill the void created by Ferguson's retirement. The Portuguese added: "I have to be an example for everybody in many aspects."
Wenger is another elder statesman in the Premier League, but last won a trophy in Mourinho's first season in charge, the 2005 FA Cup. Nevertheless, Mourinho still considers Arsenal rivals. "They are contenders," Mourinho said. "They will sign some players that will improve the team."
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