Oleh Husyev's early goal gave Dynamo a deserved lead as Everton made a poor start to the first leg of the last 16 UEFA Europa League tie.
But Steven Naismith levelled proceedings six minutes before the break and Romelu Lukaku netted a late penalty for the Premier League outfit.
Everton's response pleased Martinez, who said: "I think it [our bad start] was [down to] the tempo that we created in our game.
"I think we were a little bit slow. I think we were a little bit cagey. And that didn't allow us to be at our best.
"After 20 minutes, we were disappointed.
"There are things that you have to do in a performance, [like] following your man in a dead-ball situation, that cost us early.
"From that point on, I thought we changed our focus, moving the ball at better speed.
"And we showed great character from that point on. That was ourselves."
Martinez is under no illusions as to how tough next week's second leg will be, though, having witnessed an impressive Dynamo performance.
Even though Everton controlled the second half, their opponents were a threat on the break and perhaps unlucky to lose after Danilo Silva was adjudged to have handled Leon Osman's cross with eight minutes left.
"I thought Dynamo defended really, really well, were very resilient," Martinez added.
"They have a lot of confidence in the way that they are.
"We are happy with the victory but we know it's going to be a really difficult 90 minutes in Kiev."
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