Moyes' tenure at United was forgettable, steering the club to their worst Premier League season ever, which saw him fail to see out the first of a six-year contract as club owners ran out of patience in April.
Martinez, meanwhile, has developed what Moyes grew over 11 years at Goodison Park, and enhanced it brilliantly - putting Everton within striking distance of the UEFA Champions League.
Despite his side beating Moyes' United 2-0 in what turned out to be the latter's last game in charge, Martinez said Moyes had enough character to return to coaching and prove his wide-ranging critics wrong.
"We know David Moyes will look forward to the next footballing chapter," the former Wigan and Swansea boss said.
"We all know he is a very successful man and has a real strong winning mentality and he will get ready to bounce back straight away.
"I am sure he will be ready to get into another job as quick as he can and I am sure he won't have a lack of offers or opportunities when you have someone who is so hard-working, focused and dedicated in his job."
Martinez was asked if anyone at Everton would be revelling in Moyes' failure after jumping ship to lead powerhouse United, but the Spaniard said there was no sadistic feeling around Goodison.
"It is not a nice situation when a manager loses his job, especially someone who has such strong links with our club," he said.
"We wish him the best of luck and he will always be well thought of and we will always be thankful of the job he did at our football club."
