The Spaniard admits the Scot "had an incredible past" at Goodison Park but wants the spotlight to be on the club's bid for a Champions League place
Moyes spent 11 years as Everton boss between 2002 and 2013, in which time he led the club to the Champions League qualifying rounds and an FA Cup final appearance, and returns to Goodison Park for the first time on Sunday.
But with Everton aiming to qualify for the Champions League for the first time since 2005, Martinez is calling on his side to concentrate on the job in hand.
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"The three points are very significant for both clubs. Once the whistle goes, that is going to be the main focus."
Moyes has endured a frustrating first campaign as Sir Alex Ferguson's successor at Old Trafford, with United on course for their worst Premier League placing, having previously never finished outside the top three.
Juan Mata arrived from Chelsea in January in a bid to revive the club's flagging fortunes, and the Spaniard has backed his new manager to turn things around next term.
"I have no doubt about it," he is quoted as saying in The Daily Mirror .
"When I joined, in all my conversations with the board and the manager about next season, they were confident about getting the right players.
"I'm sure this club is going to come back and fight for every trophy. Since I was a kid, Manchester United was fighting for everything, and this moment is going to come back for sure."
United come into the game in seventh, nine points behind their fifth-placed opponents, with Everton fans enjoying a fine season under Martinez.
Everton have enjoyed a resurgence under Martinez that has seen them pick up impressive home wins over Chelsea and Arsenal, while a 1-0 triumph at Old Trafford earlier in the season highlighted the advances they have made with the Spaniard.
Wednesday's surprise 3-2 home defeat to Crystal Palace left them one point behind Arsene Wenger's men with four games to go, and they will continue to be without Steven Pienaar (knee) on Sunday, while Phil Jagielka (hamstring) could be fit enough for a place on the bench.
Robin van Persie will once again be missing for United due to a knee injury, but former Everton pair Wayne Rooney (toe) and Marouane Fellaini (knock) are expected to feature.