A 1-1 draw with Arsenal on Sunday left United facing a likely fourth-place finish in the Premier League, which will send the team into the final qualifying round of the Champions League. And that could mean potential matchups against opposition like Valencia and Monaco to reach the group stage.
"It is always stressful," United manager Louis van Gaal said. "You can meet an opponent who is halfway through a season already. It is not so easy. But I am satisfied we have set our goal (of the top four) and reached that."
Tyler Blackett's late own-goal earned Arsenal a point that kept it in third place, two points ahead of United. Arsenal will secure a top-three finish by winning one of its last two matches — first against Sunderland on Wednesday and then against West Bromwich Albion on Sunday in the final round of the league.
Arsenal has gone through the Champions League's qualifying round for the last two seasons and manager Arsene Wenger will be glad to see the back of it.
"It takes the pressure off the holidays," he said. "We have always that in mind when you prepare (for a new season) and it will be great when we do it. But it is still to do."
Ander Herrera opened the scoring for United in the 30th minute, sidefooting home a volley from Ashley Young's cross.
Manchester City is favourite to finish second behind Chelsea after beating Swansea 4-2 to move five points ahead of Arsenal, having played a game more.
City has won its last five games and its attacking swagger has returned, with 10 goals coming in the team's last two games. City has ensured qualification for the Champions League's group stage and a home win over Southampton will secure second place.
Wilfried Bony scored in stoppage time on his first return to Swansea since moving to City in January, while Yaya Toure scored two goals and James Milner added the other.
"I feel it's like my garden here. I know the pitch here so well," Bony said. "It was a strange moment when I scored. This team did a lot for me — and the fans too."
Swansea came from 2-0 down to pull level thanks to goals by Gylfi Sigurdsson and Bafetimbi Gomis, but conceded twice in the final 16 minutes. The Welsh team will definitely finish eighth and cannot now qualify for the Europa League.
At Old Trafford, United may have bid farewell to its top-three hopes — and also might have said goodbye to its goalkeeper David de Gea.
The Spain international hobbled off with a hamstring injury in the second half and is set to miss United's last match of the season, against Hull.
With Van Gaal acknowledging it will be hard to keep De Gea amid interest from Real Madrid, United's best player this season may have played his last game for the club.
"He is Spanish, he is Spanish international, now a Spanish club is coming, his girlfriend is Spanish, his father and mother come every week or every two weeks here. So it is difficult," Van Gaal said.
Radamel Falcao could also have played his last game at Old Trafford. The Colombia striker, who is on loan from Monaco, offered a little wave to the crowd after being substituted after 60 minutes and Van Gaal gave no assurance Falcao would be back next season.