After playing a brilliant first half, the Toffees withstood intense pressure from the hosts in the second to come away with a well-earned point, prompting praise from their boss.
Following the game, Martinez said: "I thought in the first half we were very good.
"I thought we controlled the game for long spells, probably more than Manchester City and we had two big moments in front of goal - Gerry Deulofeu's chance and Leon Osman with an incredible bit of technical ability.
"The second half was a little different.
"We found it difficult to impose ourselves but we had to show resilience and concentration and defend well."