With the quarter-final delicately poised at 1-1 after Romelu Lukaku cancelled out Mesut Ozil's opener, Gareth Barry was penalised for tripping Alex Oxlade-Chamberlain inside the penalty area.
Former Everton midfielder Mikel Arteta put Arsenal back in front from the spot, then Olivier Giroud added a brace as Arsene Wenger's men boosted their hopes of ending their nine-year trophy drought with a 4-1 victory at Emirates Stadium.
However, Martinez felt the penalty awarded by Mark Clattenburg was generous for the London club and a pivotal moment in the tie.
"I still feel the penalty is a very soft call," he told ITV.
"It's the key moment and I felt obviously it's a situation where Gareth is fighting with him for the ball. There is contact but is there enough contact for a penalty?
"The second goal was going to change the game competely. That second goal was vital, we wanted to make sure we had the opportunity to score that."
The defeat extended Everton's winless run on the road against Arsenal to 20 matches in all competitions as Martinez's hopes of becoming the first manager to win back-to-back FA Cups with different clubs were ended.
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