Stones was attacked in the media for his performance in last week's League Cup semi-final defeat by Manchester City.
He was also at fault for the opening goal as Everton lost 2-1 to Swansea City last month and conceded a last-minute penalty in a 4-3 reverse at Stoke City's hands in December.
"When you reach the level John has you are going to be scrutinised and John understands that. He is working very hard to keep himself fit and to produce his best level," Martinez told a news conference.
"He has had an incredible season so far for a young man. He has been through a lot in the last eight months and has been incredibly professional throughout and is growing all the time. It is not an issue."
Martinez was speaking after Everton sealed one of the costliest signings of the mid-season window when Oumar Niasse joined in a 13.5 million pounds move from Lokomotiv Moscow on Monday.
The manager said the Senegal striker was not bought to act as a deputy for Romelu Lukaku who has scored 15 league goals this term.
"He is not back up. He has his own ability and is someone who can stretch a defence," Martinez said.
"He had a real desire to join us... he has incredible hunger and will fit into our dressing room."
Everton have won just three of their 12 home league games this season and only bottom club Aston Villa, who have one victory in 11, have a worse record.
"It's true our points return at home hasn't been good enough. I think we can correct that. We need to be solid in terms of leaking goals that have cost us," said Martinez.
Everton, who are 12th in the table, host third from bottom Newcastle United in the league on Wednesday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Tony Jimenez)
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