Everton were exceptional at times against the Premier League leaders and enjoyed the majority of possession in an exciting game at Emirates Stadium.
However, it looked like they might leave empty-handed after Mesut Ozil opened the scoring for Arsenal with just 10 minutes remaining.
Substitute Gerard Deulofeu quickly equalised for Everton, leaving Martinez proud of his team's display if not entirely satisfied with the result.
"The performance - I couldn't be happier," Martinez told Sky Sports.
"The only bit of criticism is you need to take your chances, in the final third we were not ruthless enough.
"But I am really, really pleased. The character is really strong.
"We conceded really late from an unlikely source but we didn't accept defeat."
The result extended Everton's unbeaten Premier League run to eight games and kept them fifth in the table, having also won at Manchester United in midweek.
Martinez added: "The draw was a fair result. For long spells we frustrated Arsenal and looked like the home team. The players deserve huge credit."
The former Wigan boss said of his mixture of youth and experience: "It is vital to have that blend.
"If you have 11 19-year-olds you wouldn't be competitive. It is a perfect blend, you need to have a team that balances each other."
Everton captain Phil Jagielka credited Ross Barkley with "keeping him young" following the Toffees' draw with Arsenal.
Jagielka sang the praises of his young team-mates, including tireless midfielder Barkley, saying: "Fantastic - on the training ground they keep us young, we've got some fantastic young lads.
"It's exciting times, he has just got to keep on doing things he does well and maybe work on things he does not do so well."
Of the game, the England defender admitted he had feared the worst when Olivier Giroud's injury-time shot rattled the bar.
"Yeah, massively," he said. "But I think we were good value for the draw.
"They had some fantastic play on the counter-attack. It was two good footballing teams and hard to get the ball back from each other."
Barkley added: "It was a fair result in the end.
"The season is going well for me; the season so far is good."
Lolz indeed Marlo there is no other club in the world that has the vociferous away support that Everton boast. real test now is to paste teams like Fulham, 3 points will do us fine but we must put them to the sword in order to capitalise on our last two performaces.- boggo