Jose Mourinho paid tribute to Zlatan Ibrahimovic ahead of his presentation as an LA Galaxy player on Friday, saying it makes him "sad" when he sees the best players head towards the end of their careers.
United confirmed Ibrahimovic had been released last Thursday amid speculation linking him with a move to Major League Soccer, ending his 20-month association with the club.
The player and Galaxy announced their agreement a day later, with Ibrahimovic to attend his first training session on Friday before a media conference.
Ibrahimovic was a leading star at Old Trafford last season, scoring 28 goals in 46 appearances, helping United to an EFL Cup and Europa League double, but in the quarter-final of the latter against Anderlecht the Swede suffered ligament damage to his right knee and saw his campaign ended early.
Although he was handed a new deal in August, Ibrahimovic only went on to play another seven games and Mourinho finds it upsetting when the best players enter their twilight years.
"For me, it's always sad when the big players go in the direction of the end," said Mourinho.
"I remember, for example, Luis Figo's last match with me and Inter, and I always remember it as one of my saddest moments.
"I feel sorry when the big ones finish or go to the last period of their careers. So, for me, Zlatan's goodbye moment was more in this direction.
"He was a top player that Europe loses forever now, because he won't be back to this level, but it's fantastic for him, a fantastic way to go.
"He won't be going from a player to an ex-player. It'll be very good for him, this period with Galaxy, these couple of years will be very good for him and American football.
"What he can do, teach, attract, his personality, passion for football. His professionalism, too, he's always had since his recovery. It was an example of what a professional should be.
"That's what MLS and US as a football country is going to get. What's more, what Zlatan is going to get will be just a way for him to enjoy the last couple of years of his football."
United host Swansea City on Saturday in a match that will be their first following the international break which, aside from an injury to Sergio Romero, Mourinho is grateful for.
"Romero is injured and I think he will be for a few weeks," he added. "In the end he was lucky because it was strong contact and will take a little while to recover from.
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"He started training with us in the last few days and he's the only one not available.
"We've recovered all the other problems we had, like Phil Jones and Marcos Rojo, who of course played with Argentina. The picture improved a lot in that aspect."