Stones was in the Everton defence, which looked solid against a West Ham attacking line-up which has caused numerous teams problems this season.
The Hammers have proven a threat for the Premier League’s best, but Everton were relatively comfortable for large stages of the match and Martinez was impressed by Stones’ display.
"It was a really interesting challenge for John, it wasn't just about defending and doing his job well, it was about leading the back four with five defenders injured," Martinez said.
"I thought John set the tone and he was immense, in the manner that you have to defend a striker like Andy Carroll and then take the responsibility in the way he started the play, I thought it was a magnificent performance."
West Ham boss Bilic was also full of praise for the youngster, who he felt dealt with Andy Carroll well.
“I like Stones - I watched one game when Everton played at Newcastle a couple of years ago," said Bilic. "He was at centre-half, and he was 20 or so, and he was magnificent.
"So good, so calm, such composure with the ball. On Saturday he did really well against Andy Carroll. He is definitely a quality player. "
The match between West Ham and Everton was an evenly contested one, which showed the strengths of both teams.
Martinez and Bilic have assembled talented squads at their respective clubs, and they appeared well matched at Upton Park.
West Ham took the lead through a brilliant strike from Manuel Lanzini, but they were pegged back when Romelu Lukaku scored an equaliser.
The draw leaves West Ham in sixth place in the Premier League table, while Everton have moved up to eighth place.