Milan lost 3-1 to leave their round of 16 hopes hanging by a thread.
Pioli said, "I think we need a mental reaction rather than a technical tactical level.
"We could have taken the lead several times during the match and this one would be different.
"As long as the team demonstrated that it could win the match, the fans were with us. It's right that the fans are disappointed, we have a duty to do better."
Asked if he'd spoken to directors, Pioli added: "Yes, yes, we talked about it in the corridors as we always do after the matches."