Wolfsburg’s Mario Mandzukic was the star of the show thanks to his two-goal haul, but Jelavic’s contribution was crucial as he restored his side’s lead just before half-time.
Speaking to reporters after the match, the Everton striker explained that hard work was the key to his prolific form, which stretches back to last season’s Premier League campaign.
“I'm happy, this was a difficult game,” he said. “Three points are vital.
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“We deserved this result and played very well. I didn't see my goal at all, I just saw the goal and one touch was enough, as always.
“It's not so difficult to transfer my form from league for the country, I'm here three years.
“It is always about giving one hundred percent, tonight I scored so that worked out.”
However, the striker refused to get too carried away after just one game, particularly when asked about his chances of finishing the tournament as top-scorer.
He added: “It's too far to think about the Golden Boot for the tournament!”
The former Rangers man also paid tribute to coach Slaven Bilic, who will step down after the tournament in order to take over at Lokomotiv Moscow.
“Bilic is great, has a lot of energy, speaks a lot with us and I'm sorry he leaves after the Euros,” he concluded.