Martinez's men looked set for defeat at Stadion Kuban on Thursday after Brazilian striker Ari put the Russian outfit ahead in the 43rd minute.
Everton lacked incisiveness for much of the encounter but salvaged a share of the spoils from the Group H game in the 82nd minute, former Cameroon striker Samuel Eto'o converting from Leighton Baines' right-wing cross.
And Martinez, whose team earned a 1-1 draw at Merseyside rivals Liverpool in similar fashion last Saturday, was effusive in his praise of the spirit of his players.
"I thought Krasnodar played really, really well," Martinez told ITV. "I was very pleased with the manner in which we stayed in the game. We showed incredible character.
"The second half we finished really, really strong. It is an incredible result for us. It was a very, very good away performance. We could have and probably should have won it at the end.
"Today was a hard-fought result away from home, Krasnodar are a side in a very good moment and they showed that today.
"For us we're still unbeaten after two games. It's pleasing."
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