A convincing 3-0 triumph at Goodison Park provided a major boost to Everton's hopes of securing a spot in next season's Champions League, lifting Martinez's men to within a point of fourth-placed Arsenal with a game in hand.
While goalscorer Romelu Lukaku played a prominent role, the likes of John Stones, early first half substitute Ross Barkley and James McCarthy also impressed as Everton made it six league wins in a row.
Martinez feels his younger players are benefiting from the presence of experienced names such as Tim Howard, Leon Osman, Sylvain Distin and Gareth Barry.
"First and foremost you need to see that the dressing room allows young players to take responsibility and allows them to grow," the Spaniard said. "[Sunday's] result just reflects the high standards these players have on the training ground.
"John Stones at 19, Romelu Lukaku at 20, Ross Barkley at 20, James McCarthy at 23 - these players showed an incredible composure and tactical awareness [against Arsenal]. I think it was a really good memory for everyone at Everton and everyone should be very, very proud of that performance."