Chelsea claimed a 3-1 win over United at Stamford Bridge on Sunday, which means United are 12 points off the west London giants, 13 behind local rivals Manchester City and a further point adrift of leaders Arsenal.
Mourinho, who has travelled to Paris to have a fragment of bone removed from his elbow following a long-standing injury, admits he cannot see United overhauling all the top three, but he hopes and thinks they will be in good shape to take fourth.
"Man United is Man United, mathematically it is possible, but it is hard," Mourinho told Sky Sports.
"It is 14 for Arsenal, but also 13 for City and 12 to us, so maybe one team might collapse, but for all three teams to collapse to do that and lose so many points, I think is difficult.
"So for them I think it is the fight to finish top four which I think they can do. It is difficult, but with that pride and tradition they will fight and hopefully they win against the other contenders as we don't play against them in the league."
The win over United was Mourinho's 100th in the Premier League, and he is the quickest in history to make that landmark, hitting it after just 142 games. Whilst he was happy to register the achievement, he insists the victory was the main thing.
"More important than anything is the three points today," he added, before admitting Chelsea enjoyed some luck in the first half. "Of course it is nice and 100 victories in the Premier League is obviously one more fantastic thing for my career, but the most important thing is really to win the match.
"It was a very difficult match, a match where it is too hard for them to be losing 2-0 at half-time. They started better than us, they were stronger than us in the beginning and we scored (the) first goal without being in control of the game and the second is too hard for them.
"In the second half we started better and had control of the game for long periods before maybe fatigue or being comfortable with the advantage. They had some spirit and initiative and with their goal the game was open but I think we deserved three points.
"It is three important points for us because it now opens a gap between us and Man United and Liverpool and we are still in contact with Arsenal and Manchester City.
"I think Man United had a good game first-half and losing like that is not easy, but I imagine they will be better and better and become the big team they are."
Mourinho was happy his decision to play Samuel Eto'o - who claimed a hat-trick - paid off so well.
"I had a strong team physically, the people at the back and David [Luiz] in front of them," he added. "And then I had the creative players and I wanted the movement around the box.
"Some of Samuel's quality around the box, and Fernando [Torres] is more about pace, about power and space, I was feeling today that United was trying to be compact and press us. I needed a player like Samuel and he works well for us, the same as Fernando."