A 1-1 draw between Lille and Krasnodar earlier on Thursday ensured progression for the Premier League side, irrespective of the result at the Volkswagen Arena in Germany.
But Everton built on their progression in style, soaking up significant spells of pressure in between Belgium international due Romelu Lukaku and Kevin Mirallas netting on the counter attack.
"It was a perfect away performance," Martinez told reporters.
"Our counter-attacks were lethal and I thought we were outstanding.
"Big credit must also go to the back five because keeping a clean sheet here is a fantastic achievement."
It was a night to remember for Everton's travelling support and Martinez thanked them for their vocal backing.
"The celebrations were incredible - there were Evertonians everywhere," he said.
"We've had phenomenal support again."
Martinez told Everton TV: "It's been a recurring problem with James' hamstring and we need to get to the bottom of it.
"He's such a high-intensity player that his soft tissue suffers a lot. He's a sprinter and we hope he didn't hurt himself too much.
"We'll assess him and see how quickly we can get him fully fit."
