The midfielder won a stoppage-time penalty to salvage a draw for the Toffees against Stoke City on Wednesday to make amends for the error that gifted Sunderland a win days earlier
The midfielder's poor backpass played in Ki Sung-Yueng, who was subsequently brought down by Tim Howard in the penalty area.
Ki sent the ball into the back of the net from the spot to bring an end to Everton's record of being unbeaten at home in 2013, but Martinez feels Osman has put the incident behind him after he came off the bench to win his side a stoppage-time penalty in the 1-1 draw at the Britannia.
"We need to remember that football is a game of risks and you're going to make mistakes, but it's how you react towards that," he said.
"I think Leon Osman is one of the most reliable footballers that you can have in the dressing room. He represents Everton and you know that, when you're facing adversity, you can rely on Leon.
"The way he's coped with what happened in the Christmas period is magnificent. I'm delighted for him. He's someone that sets the standards on a daily basis."