The Scot had been in the job for less than a year, but under his management last season's Champions have slipped to seventh in the Premier League and will not participate in next year's Champions League as a result.
With that in mind, former United trainee Savage believes that the club were left with little option but to part company with the 50-year-old.
"I think it is the right decision. What you can't legislate for is the champions being seventh. If they were third or fourth an playing attractive football you could argue to give him more time," he told BBC Sport.
During his time at the club, United lost 15 matches in all competitions.