“It’s an incredible night, the kind we dreamed of. It has been a long time since I had played such a match and we have shown that Inter are ready for the big matches,” Martinez told Sky Sport Italia.
“I am very happy for the team, which is playing well and growing match after match.”
Shakhtar dominated possession as expected but were toothless up front and Inter opened the scoring with their first chance after 19 minutes.
Nicolo Barella collected a woeful clearance from goalkeeper Andriy Pyatov and raced down the right flank before crossing for Martinez, whose perfectly-timed header went into the back of the net.
Seeking their first trophy since a 2011 Coppa Italia triumph, Inter controlled Shakhtar, who pinged the ball around without being able to bring it forward before the 43rd minute, when Marcos Antonio fired a shot just over the bar.
Pyatov made up for his earlier mistake with a superb save four minutes into the second half, tipping the ball wide to deny Martinez who had attempted a fine loop from 30 metres.
Shakhtar, who had not mustered a single shot on target in the first half, still failed to threaten after the break until the 62nd minute when Junior Morales headed the ball straight at Samir Handanovic.
“We’ve had a great campaign in Europe but this result was a big disappointment. We couldn’t show our football. Their second goal destroyed us mentally,” said Shakhtar’s Davit Khocholava.
“Inter have two fantastic strikers. It was very hard to play against them in one-on-one situations.”
Inter were just more clinical.
Two minutes later, D’Ambrosio headed home from Barella’s corner to make it 2-0.
Martinez curled in a perfect shot in the 74th to cap a remarkable individual performance, dashing any hope of a comeback by Shakhtar.
Martinez, who before his brace had not previously scored in the competition, then turned provider, releasing Lukaku on the right for the Belgian striker to make it 4-0 from inside the box.
Lukaku has now scored in 10 consecutive Europa League matches and by producing another cool finish at the end of powerful run seven minutes from time, he is now one short of Ronaldo’s mark of 34 goals in one season for Inter in 1997-98.
“We are a team that is growing day by day, there are both young and experienced players. This is fundamental in a team, so the less experienced can follow those who have more experience,” added Martinez.
“Sevilla are a strong team. We will try to prepare as best we can for this match, we hope that everything goes well and that the Cup can go to Inter.”