Sunderland - Louis van Gaal admitted that Champions League qualification will be "very difficult" after a shock 2-1 defeat at second-bottom Sunderland increased the pressure on the Manchester United manager.
A late own goal from goalkeeper David de Gea at the Stadium of Light on Saturday condemned United to a first loss in the league on Wearside for 19 years.
It leaves the 20-time English champions six points adrift of the top four with 12 games remaining after a display described by captain Wayne Rooney as "not good enough".
Anthony Martial's 10th goal of the season pulled United level before half-time, cancelling out Wahbi Khazri's opener, but Sunderland were worthy winners.
Their success will intensify the uncertainty over Van Gaal's future, with speculation mounting that former Chelsea manager Jose Mourinho is set to replace the beleaguered Dutchman at the season's end.
Van Gaal conceded that a top-four finish is the "minimum requirement" for a club of United's stature and vast resources.
But with that now looking increasingly unlikely, he said: "We needed so much the points, so in the circumstances we're in, this is very disappointing. I can't say it any other way.
"If Wayne has said it will be difficult for us to finish in the top four, then I agree with him. It's going to be very difficult now with the gap. It's still possible, but it's very difficult.
"We needed to win this game. We want to be in the top four and now it will be very difficult. That's our aim, the minimum requirement for a club like this. You can't close your eyes to this."
United can also qualify for the Champions League by winning the Europa League.
They travel to Danish side FC Midtjylland in the last 32 of the competition on Thursday and Van Gaal added: "You can say OK, that's the other way to qualify. But there are some very good sides left in that competition."
Van Gaal, who revealed that defender Matteo Darmian had suffered a dislocated left shoulder after being forced off before the interval, admitted that his players had failed to cope with Sunderland's physical approach.
United have taken just six points from the last 21 available in away league games and won three of their last 13 top-flight matches.
"We couldn't deal with the aggressive pressure from Sunderland," Van Gaal said. "We knew the danger they posed from set-plays, but we were very bad for the first 25 minutes.
"It's not a question of being let down by the players. They want to deliver. Because they didn't deliver today (Saturday), you're disappointed and frustrated, but we're working together. We're pulling at the same strings.
"Unfortunately, Darmian is a dislocation and he's out for several weeks. We don't have any more full-backs."