Louis van Gaal thinks Manchester United will have to win their last four league games to have a chance of a top four finish.
An early Damien Delaney own goal and a cracking effort from Matteo Darmian meant that United closed the gap on Arsenal in fourth to just one point while City are two points ahead of them in third.
United remaining fixtures are against Leicester (h), Norwich (a), West Ham (a) and Bournemouth (h).
When asked whether his team have put pressure on Arsenal and Man City, Van Gaal said: "We are putting pressure on them throughout the season. At the end of the season it counts much more. I'm very happy. We have four matches to go and we must win them all. Then we have a chance."
United enjoyed 66 per cent possession in the victory and registered 10 shots on target, forcing Julian Speroni into making a number of top saves.
Van Gaal's team have been widely criticised this season for playing too conservative at a pedestrian tempo but the manager insists United have attacked in "every game."
He said: "I want to always play attacking football. In this season we have attacked in every game but maybe in a slow tempo sometimes. Our opponents have received playing a compact defence - it's not so simple to disorganise our opponents, but today we did it."