The Welshman was asked to take the reins for the end of the 2013-14 campaign when the club ended the tenure of David Moyes.
United, however, decided the time was not right for Giggs to have the role on a permanent basis and opted for the experience of current Netherlands coach Louis van Gaal, who will take over at Old Trafford after the FIFA World Cup.
Giggs subsequently retired from playing and accepted the position of assistant manager.
The 40-year-old is looking forward to working with Van Gaal, and believes his brief managerial stint will bode well for the future.
"It's been a whirlwind and I wouldn't change it for the world," said Giggs, speaking in an ITV documentary, Life of Ryan: Caretaker Manager.
"It was just a brilliant experience, one that I thoroughly enjoyed and will be all the better for next time it happens.
"I met Louis and the meeting went really well. I liked him instantly and I'm looking forward to working with him and learning from him."
Giggs, who won 13 Premier League titles and two UEFA Champions League medals as a player at United, also admitted that he broke down in tears after United's final game of the season with Southampton as he thought his lengthy association with the club was coming to an end.
He added: "We got off the plane at Manchester Airport and I was saying goodbye to the players, thanking them.
"Potentially saying goodbye to a lot of players for the last time, a bit of the staff, and I'm not an emotional person. Well, I didn't think I was.
"My car was parked right outside and I thought, 'I need to get in my car here'. I could feel myself getting emotional.
"So I get in my car and I just went, started crying, started getting really emotional and I think it was just a mixture of what I've just said, saying goodbye to people for maybe the last time, and the pressure that I put myself under.
"It sounds stupid now, but it's just not me, it's just not me at all."
