The Scot was dismissed on Tuesday following a miserable spell in charge at Old Trafford, with a defeat by Everton his last act at a club he only joined last summer.
The pressures of working at United are known to Sbragia, now manager of Scotland's Under-19 side. He has this week been working with his squad at a training camp ahead of next month's European Championship Elite Round in England and has admitted that he was taken aback to learn that Moyes had been dismissed.
Sbragia - who was sacked as Sunderland manager in 2009, despite saving the club from relegation the season before - believes that Moyes had inherited a long-term project and that the United hierarchy moved too quickly to move him on.
"I don't think it was long enough," said Sbragia, who served as reserve team coach at Old Trafford between 2002 and 2005. "He was on a six-year contract, so it was a six-year plan he would have had. Listen, it's nice to get up and running right away but sometimes it's difficult.
"What happens if they bring in another manager and he doesn't do well in the first 10 months, do you get rid of him? I personally think they should have stuck with Davie Moyes. He was in a settling-in period as well, remember. Getting to know the players, the club, the staff. So I'm sad to see him go."
The pressure on Moyes to make an immediate impression had been unrelenting, particularly as he was following on from Sir Alex Ferguson. Sbragia acknowledged that the doyen of Scottish coaching was not a big hit in his first few months at Old Trafford either.
"It's happened to many managers where they have gone in and not done well and then a year later . . . look at Alex Ferguson when he went in at Manchester United," he added. "He didn't do particularly well at first because it's just about rebuilding the club.
"I thought they should have given [Moyes] two or three years and then looked at the bigger picture. But they've made a decision."