Giggs, 40, took charge of the first team for the last four matches of the campaign after David Moyes was sacked and will work under incoming manager Louis van Gaal from next season.
The Welshman, who recently announced his retirement as a player, said that the emotion of managing the team caught up with him after they drew 1-1 at Southampton on the final day of the Premier League season.
"We got off the plane at Manchester Airport and I was saying goodbye to the players, thanking them and potentially saying goodbye to a lot of players for the last time," he said in a documentary due to be broadcast on ITV on Thursday.
"I'm not an emotional man -- well, I didn't think I was -- but 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 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.
"I come out the airport at the lights and (United coach and former team-mate) Nicky Butt just pulled up next to me and I'm thinking, 'I can't let Butty know that I've just been crying.' So I just give him a little wave and looked the other way and waited for the lights to go green.
"It sounds stupid now but it's just not me, it's just not me at all. Driving home from the airport was a release.
"It was a sort of strange feeling, knowing that I didn't have to come in tomorrow and that it's a new beginning and it's exciting. For the first time in my career, it's going into what is going to be a different season, a different summer."
- 'Life isn't like that' -
Giggs
said that his experience in the Old Trafford dug-out would stand him in
good stead for his own future career as a manager and expressed
enthusiasm about working alongside current Netherlands coach Van Gaal.
"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
said.
"It's been a whirlwind and I wouldn't change it for the
world. It was just a brilliant experience and one that I thoroughly
enjoyed and will be all the better for next time it happens."
While
Giggs admitted to harbouring some regrets about his final season as a
player, he said that he had jumped at the chance to become interim
manager.
"It's been a difficult year, playing-wise," said Giggs,
who made a record 963 appearances for United. "(I've) not enjoyed the
results and the playing, so have I contributed? Not as much as I have
done previously.
"If I'd have retired last year I'd have gone out
on a high: it was the 20th (league) title and everything would have been
rosy, but life isn't like that."
He added: "I took the manager's job without hesitation, because who turns the chance of managing Manchester United down?
"For
20 years Sir Alex (Ferguson) used to say, 'Wait until all you lot are
managers and you'll find out how hard it is to pick a team, to leave
good players out,' and I was just sat there going, 'Yeah, yeah, yeah,
whatever.'
"And it's like having your first baby. You can prep as
much as you can, but until it comes down to actually living it day in,
day out, you can never prepare for it."