The German outfit went into their final group game at Benfica on Tuesday sure of their place in the last 16 and knowing victory would guarantee top spot.
But Schmidt's side missed out on securing an easier passage to the quarter-finals as they were held 0-0 in Portugal while Monaco beat Zenit 2-0 to advance as group winners.
"It is a pity, a goal would have been enough for first place," Schmidt told the club's official website.
"But we want to learn from this game.
"My team has tried everything, especially in the second half, to win the game."
Benfica could not climb off the bottom of the group regardless of the result and coach Jorge Jesus' starting line-up reflected this, retaining just one player from the weekend win against Belenenses.
Leverkusen also left out regulars Son Heung-min and Stefan Kiessling before calling on them to find a winner in the final 20 minutes, but by that time it was too late.
"In the first half, Benfica had too much space," Leverkusen captain Simon Rolfes told the club's official website.
"After the break we improved a bit and played better together. But we did not deserve to win."
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