Win over Arsenal 'perfect night' to finish Man Utd career – Carrick
Michael Carrick says he is leaving Manchester United after the end of his spell as caretaker manager.
Carrick, in charge for three matches, announced his decision after United's 3-2 win over Arsenal on Thursday.
"After a lot of thought and deliberation, I have decided that now is the right time for me to leave," said Carrick.
Ralf Rangnick has been appointed interim manager until the end of the season.
Carrick, a five-time Premier League winner during 12 years as a player at United, took over as caretaker boss after Ole Gunnar Solskjaer was sacked on 21 November.
He took charge of the 2-0 Champions League away win to Villarreal on 23 November before dropping Cristiano Ronaldo to the substitutes bench for the 1-1 draw at Chelsea last Sunday.
Carrick announced his decision to leave minutes after the Arsenal victory which lifted United into seventh spot in the table.
"It wasn't easy telling the players," he added. "In some ways you feel like you're leaving them in the lurch but sometimes you have to do what's right.
"I've loved working with them – they are a terrific group of players."
Michael Carrick was first-team coach under Ole Gunnar Solskjaer (right)
'Loyalty to Solskjaer was a bit of a factor'
Carrick, who also helped United win the Champions League in 2008, was first-team coach under Solskjaer.
The 40-year-old said that loyalty to his former Red Devils team-mate was a "little bit of a factor" behind his decision to leave.
"It's not been an easy decision to make but I feel it's the right one," Carrick added.
"It's 100% my decision. Over the last week I was conscious I respected the club and the manager coming in. I thought it was the right thing to do for the club and for Ralf. I'm quite happy with that.
"The loyalty to Ole is a little bit of a factor but there were a lot of things that came into my decision."
Michael Carrick oversaw two wins and a draw in his three games as caretaker following Ole Gunnar Solskjaer's sacking
Speaking to BBC Sport, Carrick added: "I was conscious of making my decision before any real conversations with Ralf. I wanted to be clear cut. It was nothing personal at all."
United midfielder Bruno Fernandes, speaking after the Arsenal win, said Carrick could become a "top manager" in the future if he pursued a career in management.
John Murtough, United's football director, said Carrick was leaving after 15 years of "exceptional service" to the club as a player and a coach.
"He will always be known as one of the finest midfielders in the history of Manchester United," he added.
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'End of an era'
Analysis: Simon Stone, BBC Sport
Michael Carrick's exit marks the end of an era at Manchester United.
Whilst many players are still around the club, working in media or as ambassadors, and two have returned in Cristiano Ronaldo and Darren Fletcher, Carrick is the last link to the 2008 Champions League team to sever ties with Old Trafford.
It was 2006 when Carrick arrived. He never deviated from the laid-back character he appeared from those first days. But that should not mask his mental strength, which helped him inherit Roy Keane's number 16 shirt and become a firm crowd favourite because of his unassuming approach and his neat passing.
Carrick is adamant he wants to spend time with his family. But in a period where Steven Gerrard has just become a Premier League manager, Frank Lampard has been one and long-time United team-mate Wayne Rooney is at Derby, it would be a major surprise if Carrick does not return to the manager's dugout in his own right.
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