Everton conceded two goals in as many first half minutes, both from routine crosses into the penalty area, with neither the back four or Tim Howard able to deal with the ball adequately.
The Toffees responded with a deflected Ross Barkley strike and built up some sustained pressure in the second half, but saw Romelu Lukaku hit the bar before Petr Cech saved superbly from Gerard Deulofeu late on.
Speaking after the game Martinez said he was pleased with his side's reaction in the second half, though he couldn't hide is obvious frustration at being in such a difficult situation in the first place.
"We shot ourselves in the foot in terms of giving away such an easy two-goal lead. We put ourselves in a really difficult position but I enjoyed the reaction and the desire to get back [in the game].
"From that point on we had two very important moments in the second half. Petr Cech made a very important save [from Deulofeu] and there was a great header from Romelu Lukaku that hit the crossbar when it looked like it was going in.
"All in all, to look like you can rescue something from the game after giving away a two-goal lead, it showed what we have in the squad but, from the other side, there is disappointment for giving away such soft goals."
"I did feel at times that we found it easy to get in good positions on the pitch and maybe having a little more know-how in front of goal, we could have used [those positions] a little better."