Martin dropped a routine cross in the final minute of the game to allow Stevenage an equaliser and could not make amends as the Dons lost in a penalty shoot-out.
Martin said: "I made a big mistake that cost us, but sometimes that happens in football.
"I've got to be big enough and strong enough to get over it.
"When you're a goalkeeper it comes with the territory that if you make a mistake it normally leads to a goal.
"I've played nearly 100 games in my career now and that was probably the lowest point, but now it's up to me to prove that I can be a great goalkeeper for this club."