Fresh from an excellent 1-0 win at Manchester United on Wednesday, Everton started superbly at the Emirates Stadium as they controlled play against the league leaders.
The visitors struggled to create clear-cut chances, though, and looked like losing when Mesut Ozil popped up at the far post to score the opener with just 10 minutes left.
But Barcelona loanee Gerard Deulofeu came off the bench to earn a draw for Everton, producing a sensational finish in the 84th minute, as Arsenal – who saw Olivier Giroud's thunderous injury-time effort hit the crossbar – could only extend their league lead to five points.
"The performance – from our point of view, I couldn't be happier," Martinez told Sky Sports.
"The only criticism is that you have to take your chances and we weren't ruthless enough, but the way we controlled the game, I haven't seen my sides come here and do it.
"It is fair to say that the draw, it is a fair result, if not, I thought we edged it in terms of controlling the game and the possession.
"For long spells we frustrated Arsenal and looked like the home team. The players deserve huge credit.
"We conceded really, really late from a very unlikely source. (But) the character of the group is undoubtedly really, really strong."
Everton captain Phil Jagielka thought his side were well worth their point and hailed Deulofeu, who had only been on the pitch for five minutes before scoring his goal.
"I think we played well for the first half," he said.
"We had a dodgy 10 minutes towards the end of it which encouraged them but I think we were more than value for the point in the end.
"Gerard came on and showed the ability and what he has got."
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