The Spaniard took Swansea into the Championship by winning the League One title in 2008, and is credited with introducing the passing style that has come to define Swansea's philosophy.
But Tate believes the club have moved on since Martinez's time at Swansea, and Saturday's third away win of the season has taken them a step nearer towards Premier League safety in their debut top-flight season.
"We've become a bigger and better squad and we're doing really well at the minute," said the ex-Manchester United player.
"We'll not be safe until game number 38. Of course we're going in the right direction and no one from outside the club is going to say we're going in the wrong direction.
Wigan anxious and tired - Martinez
"We've come into this league and no one expected us to do as well as we've done.
"I think people were writing us off before the beginning of the season and we knew within the dressing room we've got a very good bunch of players."
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