It seems as though Stones, 21, has been earmarked by Premier League champions Chelsea as a potential long-term replacement for former England captain John Terry.
"John has incredible potential going forward and I can see a future England captain," Martinez told Sky Sports.
"I think that pressure and speculation, he is taking it in an incredible way. I think every single Evertonian will show respect towards him because the way he's handled things in a very difficult position shows the potential that he has."
Stones marshalled Everton's back four as they repelled waves of Tottenham attacks, reading the game superbly and showing nerveless ability on the ball.
"I thought he was an immense influence on what we did defensively," Martinez added.
"He's composed on the ball and he looks like a player that has grown over the last four or five weeks."
Everton have constantly reiterated their reluctance to sell Stones to Chelsea who suffered a shock 2-1 home defeat by Crystal Palace on Saturday.
"As a football club we are very clear in our ambitions and vision," Martinez said. "We've been working really hard in the last two years to keep a core of players, to develop young players, to give them a big role.
"As a football club we need to make sure we allow these types of players to evolve and become a winning team. We've got one of the strongest chairmen (Bill Kenwright) in allowing us to build a project and build a team."
Everton have five points from four league matches this season while Spurs are on three.
(Reporting by Tom Hayward, editing by Tony Jimenez)
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