The forward scored on his tournament debut for die Mannschaft in the quarter-final against Greece, before coming off the bench at half time in the semi-final against Italy.
"Marco's performances stand out beyond doubt," Klopp told Welt am Sonntag.
"His quality, coupled with our patience, is a good combination. He does not need to score four goals in his first game.
"We want to help him become the player we see in him, who will be better than the one at [former club Borussia] Monchengladbach."
Asked what his stance was regarding the €17 million fee that BVB had to pay in order to prise him away from his former club - the highest fee ever received by Monchengladbach - Klopp was stoical.
"In football there is only one principle, and that is not based on transfer fees, but on performances. We have paid €17m for him and he is worth the money."