The Scotsman lasted less than 10 months at Old Trafford since taking over from Sir Alex Ferguson, who chose Moyes as his successor after announcing his retirement last summer.
The Red Devils announced on Tuesday that they had parted company with Moyes, but Martinez, who replaced the Scotsman at Everton last summer, believes that the coach will "bounce back".
"There has been a lot of talk over the matter," Martinez told reporters in Thursday's press conference. "It is not a nice situation when a manager loses his job.
"We know Moyes will look forward to the next football chapter and the next experience. He is a strong man with a winning mentality and I am sure he will bounce back straight away. He has ensured he will be ready to get into another job as quick as he can. He won't have the lack of opportunities."
After sacking Moyes, United appointed Ryan Giggs as interim coach until the end of the season.