The 50-year-old was given the task of succeeding Sir Alex Ferguson at Old Trafford last May but was dismissed from his post on Tuesday after just 10 months in the job.
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"I was a little surprised because Manchester United don't have that custom of sacking managers," he told reporters.
"In another club, it would be completely normal but, after so many years with Sir Alex, it is a little surprising.
"I feel for Moyes but this is the life of a coach. At time things don't go well and you are sacked. I'm sure Moyes will look for and find another job."
A 2-0 loss to Everton on Sunday ensured that United, who sit seventh in the Premier League, cannot qualify for next season's Champions League.
Club legend Ryan Giggs will take charge of the team for their remaining games this season.