Thursday's stalemate at the Etihad Stadium left United just a point below local foes City, who occupy the Premier League's fourth and final Champions League qualifying berth.
But Mourinho believes Liverpool, two points above United in third having played a game more, and Arsenal, four points below them having played a game less, are now their principal rivals.
"I think Man City is going to finish top four," the United manager said.
"The matches they have to play, I see them doing that. I think it's between us, Arsenal and Liverpool."
While United's run-in features successive trips to Arsenal and second-place Tottenham Hotspur, City's is more benign, a home game with eighth-place West Bromwich Albion their most arduous test.
United are also besieged by injuries and will now be without midfielder Marouane Fellaini for three games after he was shown an 84th-minute red card for headbutting Sergio Aguero.
Phil Jones, Chris Smalling, Marcos Rojo, Paul Pogba, Juan Mata and Zlatan Ibrahimovic are all sidelined and Timothy Fosu-Mensah picked up an injury after coming on in place of Henrikh Mkhitaryan.
With a two-legged Europa League semi-final against Celta Vigo also looming on United's horizon, Mourinho admitted his squad is being stretched to its limits.
"We have played 18 more matches than Liverpool," said the Portuguese, who side equalled the club record of 24 successive top-flight games without defeat.
"Eighteen more matches is like half of a Premier League, almost. Eighteen matches are many miles in the players' legs. So if you can say that, it's an unfair fight.
"But we are going for that. We have the semi-final on Thursday. We have a match (at home to Swansea City) Sunday, 12 o'clock.
"We lost two more players today, Fellaini and Timo Mensah, because he has also an important injury in the last action of the game.
"I don't think we (will) recover any of the others. But we go for it, we fight.
"Twenty-four matches in the Premier League is a lot. The guys have an amazing spirit and here we go again, Sunday."
