The former Chelsea forward was quoted last week highlighting his desire to return to a "top club", but he put aside talk over his future with a fine display in Switzerland.
With Everton now on the brink of reaching the last 16 of the competition, manager Martinez - who saw his side fall behind early on - singled out Lukaku's display.
"I have always said that Romelu Lukaku is an important player for us," the Spaniard said. "He ticks every box - he is the complete striker.
"When you see us play like that, we get back to memories of last season. In the league we have felt cagey. Europe is a fresh challenge."
The visitors had John Stones sent off just past the hour mark, with Young Boys goalscorer Guillaume Hoarau - who broke the deadlock after 10 minutes - missing the resulting penalty.
Martinez feels Stones will heed the lesson of his dismissal and was pleased with the way his men responded to going behind.
"John Stones will learn from his sending off," he added. "It will help him in the long run. Even with 10 men we were positive.
"It was a test of character to go behind to a team in great form at home. It was a great result."
Everton will host the return leg at Goodison Park next Thursday.
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