The Bundesliga outfit qualified for the UEFA Champions League's knockout stages earlier on Wednesday after Zenit beat Benfica 1-0.
But Leverkusen missed the chance to secure top spot in the group, despite dominating the Group C contest.
The hosts spurned a host of chances and were made to pay when Monaco substitute Lucas Ocampos netted in the 72nd minute.
Ocampos' goal moved Monaco to second in the pool, one point behind Leverkusen, and the third-placed Zenit can also still qualify - setting up an exciting matchday six.
"We played better than our opponent but that is football," Rolfes said.
"After the break, when we were dominant, we missed the chance to take the lead."
Leverkusen forward Stefan Kiessling added that the result was "very annoying".
The German side visit fourth-placed Benfica on matchday six.
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