PSG reached the semifinals 5-4 on aggregate, though lost the second-leg at Villa Park 3-2, despite being 2-0 ahead inside the opening half-hour.
"You have to be demanding in these matches, we made it very difficult for ourselves in the second half when we let up. We thought we'd qualified, we thought we were too good to go out.
"At 2-1, we thought it was over, but that's how the Champions League is," he told Canal+.
Dembele emphasised they will have to use the hectic end to the match as a lesson for the semifinals.
He said: "You can play against teams in front of their home crowd with a heated crowd that turns the match around, we'll have to be more vigilant."
Dembélé nevertheless wanted to end on a more positive note.
He added, "We qualified, we're happy, for that now we have to get back to work to win this trophy. Once again, PSG are in the semifinals, which is good for the club and the league, and we'll do our best to reach the final."