Everton had strong claims for a penalty turned down in the first half when Leighton Baines went down in the box under a challenge from Cardiff midfielder Gary Medel, but referee Anthony Taylor waved away their appeals.
Martinez admits he feels his players did not contest the decision too much as they were shocked at the penalty not being awarded.
"In that incident you get a little bit of a shocked reaction," Martinez told Sky Sports. "Gary Medel goes to ground and doesn't get close to the football.
"I thought the referee had his view blocked as I could not explain it any other way, from my point of view and the fourth official's viewpoint it was a clear penalty.
"Leighton was impeded, if he carries on he's in a great position and he doesn't need to go down and obviously they are big moments because I though the first goal today would be very significant and that moment is a clear decision."
Despite the penalty call going against his side Martinez was happy with his side's display as they kept Cardiff at bay.
"I am satisfied with our defensive display because I think any team that comes to Cardiff will have to be well aware of the strength of his Cardiff side and I thought we nullified that and we stopped them from being a real threat in the game," added Martinez.
"Sometimes just that good decision or good bounce of the ball you need that, but overall from our point of view we probably deserved all three points."