Spain were left frustrated after they were held to a 1-1 draw by Greece in their opening 2022 World Cup qualifying Group B fixture on Thursday.
Alvaro Morata opened the scoring from close range for the hosts after 32 minutes, moments after Dani Olmo had rattled the crossbar from distance.
However, Martinez disputed the validity of the call and wondered what might have happened if VAR was in use during the match.
"Obviously, I'm really angry. It's a moment that they make you pay for. We're not happy with the draw and with VAR it would've been a different story," Martinez said.
"It's a 50-50 challenge and I get there. I can't stop myself. I pull my leg away and I don't mean to do any damage. He was clever and stayed down, and it's strange the referee took so long to blow for it, too. It was the key moment in the game."
Anastasios Bakasetas went on to smash the ball in from the spot to stun Luis Enrique's side.
"I'm not a fan of the result at all, we lacked that little bit of inspiration," Luis Enrique said. "What I did like was the attitude and the rhythm of the players; but when we got close to Greece's box we weren't at it.
"We need to create more danger. We force the opponent back into their box but we just didn't have the spark or create the chance you need to make at this level."
Morata spurned his country's best opportunity for a winner as he headed straight at the goalkeeper as Spain dominated possession but struggled to create any clear chances against the resolute visitors.
Spain travel to Georgia in their second qualifier on Sunday, the same day Greece host Honduras in a friendly.