The Toffees had the better of the contest at Cardiff City Stadium but could not convert their best chances against a gritty Bluebirds side as they picked up a third consecutive point.
Kevin Mirallas wasted two great chances and David Marshall brilliantly saved a deflected Nikica Jelavic header, while the visitors were also left scratching their heads at how they were not awarded a first-half penalty for Gary Medel's rash challenge on Leighton Baines.
The Chile international appeared to foul the left-back as he raced into the area three minutes before half-time, but referee Anthony Taylor gave only a goal-kick.
Martinez said: "From the angle I was at it looked a real clear, stonewall penalty.
"Leighton said it was a clear penalty. He was trying to get into the box and there was a challenge where he doesn't get the ball. It's as clear a penalty you will ever see.
"The last thing I would do is come out and just blame the referee for not getting the three points, but it was a key moment. The first goal would have been significant in this type of game."
Martinez fielded Baines and fellow Manchester United target Marouane Fellaini against the Bluebirds, and both played 90 minutes with the close of the transfer window just two days away.
The Spaniard has made it clear he wants to keep hold of the pair, and confirmed there has been no new offer from United for them.
He said: "They are top players as you have seen today and I want to keep my top players. But when you are in the transfer window you are not in control of what is going to happen.