Jose Mourinho insisted that his side put in a solid performance against a “sad” Sunderland team as they won 3-0 at the Stadium of Light.
Zlatan Ibrahimovic, Henrikh Mkitaryan and Marcus Rashford all scored as the Red Devils eased past struggling Sunderland.
Mourinho was pleased his side had secured three points after Liverpool and Manchester City – the teams in third and fourth in the table – both won on Saturday.
He said: “After Liverpool and Manchester City’s victories, if we didn’t win today it’s almost mathematically impossible (to finish fourth).
“It was important for us to win and that was the main objective.
“We did that and, apart from that, there were no more injuries to add to the difficult list we have, because we don’t hide that we are still fighting for our situation in the Premier League.
“But the Europa League becomes fundamental for us, it’s the only competition we can win now.
“We did the Community Shield, we did the League Cup. The Premier League, no way, so it is our competition to fight for.”
Victory on Wearside was secured by Zlatan Ibrahimovic’s stunning 30th-minute strike and, after Sebastian Larsson had been controversially dismissed by referee Craig Pawson for a challenge on Ander Herrera, second-half goals from Henrikh Mkhitaryan and substitute Marcus Rashford.
But it was full-back Shaw, criticised roundly by Mourinho in recent weeks, who earned a pat on the back from the Portuguese following a composed display.
He was taken off just after the hour following an early caution.
He said: “He played well, played solid. The opposition was not creating big problems, but he was solid and was confident with the ball.
“He was going forward with some danger, he was reading the game well to go when Mkhitaryan went inside. He played really well, so it was a good hour for him.
“I thought about a half-time change, but thought it was too harsh for him.
“I wanted him to play a little bit more, so at 2-0, one hour in, with the crowd asking for everything and putting the referee under a little bit of pressure, no risk (taken).
“We have no players, we need him to be available for the next match.”