In a difficult first-half, the Eagles fell two goals behind after an own goal from Jefferson Lerma and a penalty from Bournemouth's Eli Junior Kroupi.
The second 45 was a much more even contest, but the hosts ended any hopes of a fightback when Brazilian teenager Rayan fired past Dean Henderson with 13 minutes left.
For Glasner, the impact of the long away trip to Kraków showed in the performance on the south coast.
"Today the tank was empty," he told Sky Sports in his post-match interview. "We could see it. The players tried and the second-half was much better, it was a game on the same level.
"First-half it was too much. We couldn't get the turnaround from Thursday evening. The players tried, but I could see it at set plays and the easy mistakes we made.
"It's not to blame anyone. It was just really overwhelming for us, this experience and the win against Shakhtar. Overall, Bournemouth were much the better team.