The Spaniard felt his side deserved their dramatic late winner which keeps the Toffees' European hopes alive but acknowledged the result would be hard for Cardiff to take
The Welsh outfit looked to have done enough to head home with a share of the spoils but couldn't prevent the Republic of Ireland defender from popping up at the death to keep all three points on Merseyside.
It was far from a vintage display from the home side but Martinez was pleased to see his players keep their concentration until the final whistle.
He said: "I was very pleased that we did not panic and continued doing the right things. It was down to the control and patience. It would have been all too easy to panic and let your heart rule your head.
"We left it late because we couldn't take our chances a little bit earlier but I think that we deserved the three points."
The former Wigan boss admitted that luck had played a huge part in the winning goal and praised Cardiff for their part in a thoroughly entertaining encounter.
Martinez continued: "I think Cardiff deserve huge credit. It was a very good performance and a little harsh on them. A couple of weeks back we were feeling the exact same way at Chelsea.
"The luck that Coleman had to miskick the ball to beat David Marshall was the way that it was going, but it was an incredible performance. To be able to still be there in the 93rd minute tells you the type of player that we have at the club."
Cardiff boss Ole Gunnar Solskjær bemoaned the decision not to award his side a penalty but could not fault the effort of his players.
He said: "Zaha weaved his way through three or four of them and [Sylvain] Distin trips him up. We can talk about it all day long but that doesn't help.
"The performance was outstanding - it was a phenomenal effort. We showed team spirit and created chances.
"We've given Everton a good game, that is encouraging but we sit here with no points and we need points."