Louis van Gaal accused his Manchester United players of being out-fought in a shock 3-nil defeat at Everton that left English football's Premier League top-four door slightly ajar for Liverpool.
Victory at Goodison Park would have all but guaranteed a return to the Champions League for United after this season's absence from Europe but they were picked off by a clinical Everton side despite hogging possession.
United missed the chance to go second and remain in fourth place.
A breakaway goal after five minutes by James McCarthy put Everton ahead and they doubled their lead before halftime with a glancing header from John Stones.
Kevin Mirallas fired Everton's third after the break to kill off the 20-times English champions and leave United seven points above fifth-placed Liverpool who have a game in hand against relegation-threatened Hull City on Wednesday.
"We have always had more fighting spirit on the pitch and I think that this is the first match that the other team have shown more of that than us," Dutchman Van Gaal said.
"We created five chances in the first half -- Marouane Fellaini had to score -- that is more than Everton."
"In the second half they scored on the counter and we had to play against a defensive side."
"This was the first match when I saw a team that was more motivated and aggressive than us. It is not good, but we are human beings."
"Everton deserved to win. When the result is fair, you can live with it."
Fellaini, who has enjoyed a better second season at Old Trafford following a miserable first campaign after leaving Everton, wasted a great chance to equalise early on and was booked for scything down Seamus Coleman.
While United are still well-placed to secure a top-four spot with four games to go, Van Gaal admitted that the result will fuel Liverpool's belief that they can still snatch fourth.
"Yes, I know that. You give the light to your opponents. I said that (to the players)."
Meanwhile Chelsea must wait at least another week for the Premier League title after drawing 0-0 with Arsenal in a niggly, physical encounter at the Emirates Stadium.
Chelsea had three penalty appeals turned down in the first half, and Arsenal one, and while the home side procured clearer chances after half-time, the result favoured the visitors, who kept their 10-point lead intact.
Victory would have enabled Jose Mourinho's team to secure the league by winning at Leicester City on Thursday but they can now claim the title in front of their own fans by beating Leicester and then defeating Crystal Palace at Stamford Bridge next Monday.
The draw ended a run of nine Arsenal wins in all competitions, but while Arsene Wenger's record of matches without victory over Mourinho now stands at 13, his side remain well placed in the race for the Champions League.
They remain third, below Manchester City on goal difference and two points above Manchester United, but have games in hand on both.