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.
"What we want to see is Marouane and Leighton to play for Everton for many, many years, not just this transfer window.
"At the moment, the situation is the same as yesterday."
Martinez would not be drawn on reports linking him with a move for Manchester City's Gareth Barry, but will look to make additions before the deadline passes.
"We are also working hard to actively identify one or two more players who could come in and help us. It's not about names because that would be very disrespectful.
"I don't like it when I hear other managers talking about players who are registered for other clubs. I'd never do it.
"The squad is strong and experienced, but it's about finding the right character to fit in."
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Cardiff boss Malky Mackay had a very different view of the penalty incident, believing it would have been a very soft spot-kick.
He said: "I have not seen it on TV, I only saw it live.
"When I saw it live I thought it would have been incredibly soft if it had been given, so I don't think it would have been a penalty.
"There was minimal contact and he (Baines) was on his way down."
But Mackay was pleased with his side's performance as they backed up their win over Manchester City with another valuable point.
He said: "We played a top team who finished sixth last season, and I reinforced to the players we could not make it a case of after the Lord Mayor's show as we would have been turned over.
"But we were at it, they were at it, and it was two teams matching each other stride for stride."
He added: "It takes huge concentration levels to keep getting in defensive positions and to have the calm needed when you have counter-attacking opportunities, and four points after three games is a very good start for us."