After dominating possession for large periods of the game, Everton pressed for a late winner, although they struggled to create too many clear-cut opportunities and were forced to settle for a point.
Bottom of the table Palace had lost their previous seven Premier League games, but Martinez says that he was always expecting a tough test from Keith Millen's side.
"We knew exactly to expect from our point of view," he told Sky Sports.
"We couldn't get that little bit of sharpness that you're looking for in the final third and probably in the first half, we had a couple of half-chances and you feel that we should have made a little bit better decisions.
"Overall, we probably allowed ourselves to get a bit frustrated. Every time the ball went out of play, it took ages to come back in and it was that sort of game.
"It was really stop-start and we couldn't really get into a position to break Palace down in their defensive set-up. They were very well organised, they worked extremely hard and they made it very, very difficult.
"In these sort of games, you usually get into this sort of role where you have to break the opposition down and then you switch off in one or two situations where you get a quick break.
"Palace were well set-up for that and at any dead-ball situation, you can lose a clean sheet.
"That was a very pleasing aspect of our play, we kept a clean sheet, we were really focused, we worked extremely hard and obviously you can understand our disappointment.
"When you have all the play that we had, you need to be able to get that final pass, that little bit of know-how, to break the team down.
"I think there were many aspects in the game that didn't allow that to happen but we couldn't have any complaints with the work rate, the focus and the concentration and how well we adapted into what we had to do."
The result was Everton's second 0-0 draw in a row, but Martinez opted to take a number of positives from the game, including another clean sheet.
He added: "You always want to win football games, there's no two ways about it, but it's important that when you don't win, you keep doing the right things and you keep clean sheets.
"I think we worked extremely hard as I've mentioned and we did really well all the way through. We worked really hard to keep the clean sheet and that's important.
"The next step is to make sure we take advantage of this situation and we get that little bit of understanding to break the deadlock and get the three points.
"It's another step towards where we're going to get and today we'll have to learn from this experience and make sure that we use it to our advantage in the rest of the season."