Samuel Eto'o's hat-trick in a 3-1 win at Stamford Bridge saw Chelsea move two points behind leaders Arsenal and a point behind second-placed Manchester City; seventh-placed United are 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 (Chelsea's rivals) to finish top four."
Mourinho, who insists Liverpool and Tottenham are still in title contention, will now ask more of his side.
"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.
"They started the match better than us and they were a bit unlucky that we scored in that moment.
"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. (On Sunday) first shot, first goal, second shot, second goal. Things were going in our direction."
Chelsea will have to improve without Fernando Torres, who faces a spell out with a knee injury.
The Spain striker, who scored at Southampton and Hull earlier this month, came on as a late substitute for Eto'o but did not last the distance due to a damage to his lateral knee ligament which means he faces "weeks" out.
Demba Ba will be given an opportunity in Torres' absence, while Eto'o was praised for his performance.
Mourinho said: "It's a pity because Nando (Torres) is in a good moment, but it's time for Demba. Next matches is for Demba or Samuel.
"It was a fantastic moment for Samuel, to score a hat-trick, and against Man United."
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.
"The important thing for me is that these 100 matches, they gave 300 points to Chelsea and especially (on Sunday) these three points are very important for us."