Klaas Jan Huntelaar scored twice and
Lyon still progressed to the knockout stage - with one match to spare - because of their superior head-to-head record over third-placed Benfica, who lost to Hapoel Tel Aviv.
But that was not enough to satisfy Puel, who is hoping to find out why his side have lost their last two matches in the pool after three opening wins.
"We missed the mark," he said. "All credit to Schalke, we failed to address and rectify the situation. It's disappointing to suffer such a result in the Champions League. We are still in the running for first place but it was a pretty poor performance and we were unable to find any answers.
"This is not a match to forget, though, because we have to rectify things and learn from our mistakes. We cannot settle for this kind of display and we have no excuses for it either.
"Instead, we must quickly find our rhythm if we are to have any kind of ambition this year. We must find our character and commitment."