Twenty-one-year-old Stones has been heavily linked with a switch to champions Chelsea throughout the transfer window, having impressed during his first two full seasons on Merseyside.
The former Barnsley centre-back played the full 90 minutes as the Toffees were held to a 2-2 draw by Watford in their Premier League opener last weekend, and Martinez was impressed with what he saw.
"I think John's performance at the weekend was really strong," the former Wigan boss said.
"I thought Phil Jagielka and him, probably with Gareth Barry, were the three players that drove the team through that difficult period we had when we went 1-0 down.
"For a young man to come up with that kind of leadership is a real sign of what he is as a footballer.
"He is a huge player for us and we're really looking forward to seeing the best of John over the next few seasons, not just the next few weeks."
The Spanish coach admits he has been flattered by the interest from fellow Premier League teams for his star players but is adamant England international Stones will not be leaving the club.
"I'll never be upset about people asking about our players. Those are compliments about players that they are performing really well and attracting interest, but nothing else.
"[But] I've said before, the player's not for sale and that's the end of it.
"We are a club that will always embrace our youngsters and give them opportunities, but in the same manner we are not a selling club and we are not are club that is going to lose its best performers."