In arguably the toughest group, Everton got a dream result in their first European match since the 2009-10 tournament.
The hosts went ahead through a 15th-minute Ricardo Rodriguez own goal which came about through a flowing passing move and the lead was doubled thanks to Seamus Coleman's close range header just before the break.
His fellow full-back Leighton Baines stretched the advantage further from the penalty spot just after the break and Kevin Mirallas' third of the season gave Everton a fourth in the final two minutes.
Rodriguez hammered in an injury time free-kick but the night belonged to Everton and Martinez was delighted with the performance.
He told ITV: "It was a really good evening. There has been a lot of talk in the last two or three days about the European nights at Goodison under the lights and it was phenomenal to see the fans supporting the team in such a special evening.
"To finish with that scoreline and performance was very pleasing.
"Going forward we were very dynamic. I thought both teams were very dynamic but we used our pressure a little bit better than them. We got a couple of good opportunities just from being really well organised high up the pitch and the work rate of the team was pheonomenal."
Martinez refuted the suggestion his side would suffer domestically if they enjoyed a deep run in the European tournament.
"We've been working really hard for 12 months to earn the right of being in the Europa League and we've got a really strong squad in terms of experience, good youth and good numbers," he said.
"We've got 25 professionals that I feel anyone can play and then we've got another group of six or seven in the under 21s and they're ready to help the first team so the more competitions, the better.
"I know we've got seven games in over three weeks but that's what the players want. And I think the mentality in the group is right for that. It's been tough tonight but it's been enjoyable."
