Ole Gunnar Solskjaer will take the 'flak' for the United loss.
Solskjaer says he leaves Manchester United with a better squad than he had and ready to kick on in the challenge for major honours.
He guided the club to second and third-place finishes in the league, but they are currently eighth, 12 points behind the leaders.
"I look back at every second here with pride," Solskjaer said.
Everyone knows I've given everything for this club. I wanted us to take the next step to challenge for the league, to win trophies, but unfortunately I couldn't get the results we needed and it's time for me to step aside.
Solskjaer replaced Jose Mourinho on an interim basis in December.
He signed a new deal with the club in July, after he was given the job full-time in March.
Solskjaer was the fourth permanent manager since Sir Alex Ferguson retired and lasted longer than the other two.
While United finished second in the league, they were 12 points behind Manchester City and lost the final on penalties.
"We were so close to Europe," said Solskjaer.
Sometimes that's the fine margin for you. I will always remember that we were close. I know the foundation is there and I'm sure they will kick on.
The signings of Jadon Sancho and Raphael Varane have not gone down well with the fans and performances have been poor.
A number of question marks had already been raised about the lack of a consistent playing style and tactics prior to the 2-0 defeat by Manchester City on 6 November.
Solskjaer thinks the club can bounce back quickly.
He said that the board and the owners supported him in bringing good people in, good players in, and that he would leave the club with a better squad.
I want the next manager to be successful and I want to support him. I know I'm good at what I'm doing, so hopefully I've laid the groundwork for that to happen.
United travel to Spain to face Villarreal in a crucial game on Tuesday, before games against Chelsea and Arsenal.
The club's technical director and two other members of Solskjaer's coaching staff will remain at the club for the time being.
