Ralf Rangnick said Manchester United "do not deserve" to play in the Champions League next season if they perform how they did against Everton for the rest of the season.
It has harmed United's chances of finishing in the top four and securing Champions League qualification.
"If we play like we did here we just don't deserve it," said Rangnick.
"The players themselves should be eager to play international football, if possible Champions League. In order to qualify for Europe you have to be able to score in 95 minutes in a game like this."
Everton came into the match following a disappointing 3-2 defeat by relegation rivals Burnley, who sit just one place below them in the table.