Louis van Gaal has said he feared his Manchester United side would struggle at Everton after watching the warm-up.
The visitors went behind after just five minutes when a counter attack culminated in James McCarthy's finish.
Goals by John Stones and Kevin Mirallas confirmed United's 3-0 loss, which the Dutchman put down to Everton having "more aggression and motivation".
"I had the feeling; the warm-up was not so good," said Van Gaal, whose concern was shared by assistant Ryan Giggs.
"In the last minutes before the game you hope you can recover and stimulate your players but then it is too late.
"You have to prepare the match already two or three days before and Everton have done that and they have won because of that."
United could have increased the gap to Liverpool in the race to secure the Champions League places with a win.
But instead they remain seven points clear of their fifth-placed rivals, having played a game more.
"This is the first match that the other team have shown more fighting spirit than us," Van Gaal added.
"Our motivation, inspiration and aggression was not as high as the opponent. When you see the first goal, three duels in a row we lost and that is an example.
"I hope it shall not happen again but, as a coach, I know it shall happen again."