Samuel Eto'o scored a hat-trick as Chelsea moved two points behind leaders Arsenal and a point behind second-placed Manchester City in a result which leaves seventh-placed United 14 points adrift of the summit.
Mourinho thinks David Moyes will be unable to overturn the deficit to all three teams in the remaining 16 games of the season and that United will not be able to retain the title Sir Alex Ferguson won before his retirement in May.
The Chelsea boss said: "It's a 14-point difference. And 13. And 12. Can they recover to one of these teams? They can.
"But to recover to three of them, it needs three teams to have almost a collapse.
"For the title it will be difficult for them. What I hope to do is they beat all of them (Chelsea's rivals) to finish top four and they beat all of them."
Mourinho insists it is not just a race between Arsenal, City and Chelsea.
"It's not just three," Mourinho said. "The distance is short. Six points from us to Liverpool. Six points to Tottenham.
"Tottenham are winning lots of matches, Liverpool too, and scoring goals. Everton, if they win tomorrow (at West Brom), they jump into that."
The win saw Mourinho extend his home unbeaten Premier League run to 71 games with his 100th win in the competition, becoming the manager to reach the landmark in the shortest time.
"I don't care about records," he added.
"I want to win the next match. This was the last match, but it's quite a coincidence: the first (Premier League win) was against Man United, the 100th was against Man United.
"The previous owner of the record was Man United manager (Ferguson), so quite a coincidence.
"The important thing for me is that these 100 matches, they gave 300 points to Chelsea and especially today these three points are very important for us."
Mourinho will demand more from his side, who started the contest second best.
"We have to improve," Mourinho said. "I want better. The first 20 minutes were not good.
"I want the game to be in our control since the beginning and it was not."
But he praised the character of his team to strike when the opportunity presented itself, unlike United.
"They started the match better than us and they were a bit unlucky that we scored in that moment," Mourinho added.
"When you are better than the opponent, you have to go and try to kill the game.
"When the opponent is better than you, you have to identify that moment, you have to be humble and you have to control the game.
"For these 20 minutes they were better than us, but my team was compact, was solid, showed solidarity. And we controlled them.
"Normally we need four, five chances to score a goal. Today first shot, first goal, second shot, second goal. Things were going in our direction."
It was not without worry and the Portuguese was particularly concerned when United substitute and goalscorer Javier Hernandez ran down Petr Cech in the second half as the Chelsea goalkeeper struggled to deal with a back-pass.
"Today was the game in my career where I was close to a heart attack," Mourinho said.
"It was not Petr Cech (at fault), it was the guy that passed to Petr Cech and Petr Cech dribbling on his own goal line."
Mourinho reserved special praise for captain John Terry for a "fantastic performance" in a match which saw United finish with their skipper, Nemanja Vidic, sent off in stoppage time.
Rafael might have followed for a two-footed lunge on Gary Cahill, but Mourinho had no complaints with the decisions of referee Phil Dowd.
"When players are frustrated, things like this can happen," Mourinho said.
"Frustration with the result, last part of the game, (Eden) Hazard was running with the ball, Nemanja fouled. It's in the limit; maybe it's an orange card.
"The kid Rafael I think is just frustration. But I think the ref was good."
Mourinho took the opportunity to criticise rival managers, who he believes should control their players better and allow officials to do their jobs.
"I don't want players to complicate the life of the referees," Mourinho said.
"It looks like other managers told (their players) exactly the opposite, and I'm not speaking about David; I'm speaking about other managers.
"Their players make the referees' lives very difficult, and because of them the referees make wrong decisions and because of them the referees are criticised.
"Maybe we need some managers' meeting with the referees, like we had in the summer, because I think some managers forgot (what was discussed)."
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