"His job at Everton deserves that - his work has been terrific," Martinez said.
But Moyes was given a hostile reception by the visiting fans during the Premier League match between the sides at Old Trafford in December, which Everton won 1-0.
"We are a club full of integrity and style, we are a proper football club, so we will show the respect to David Moyes and what he's done at our football club," said Martinez.
"We all know he's the Manchester United manager now and I'm sure that reception will be very much different, but every Evertonian has got great memories of the job that he did."
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