Moyes lasted just 10 months at Old Trafford after leaving Everton to join United.
But his replacement at Goodison Park has backed him to return to the top of the game soon.
Martinez said: "[There] has been a lot of talk over what has happened.
"It's not a nice situation when a manager loses his job, especially one with such strong links to our club.
"But he will look forward to the next chapter - he's a very successful man with a winning mentality and will bounce back.
"Of course lots of clubs will be willing to take him on - someone with all that experience at the highest level and the know-how, it's a real strength.
"He will be ready to get into a new job as quickly as he can."
Martinez has ruled Sylvain Distin out of Everton's trip to Southampton on Saturday and Phil
