Palace took charge of their quarter-final with a 3-0 first-leg win at Selhurst Park.
Jean-Philippe Mateta scored his first goal since New Year's Day with a first-half penalty, then Tyrick Mitchell doubled the advantage after Mateta's effort was saved, and Ismaila Sarr scored a late third for the resounding win.
“More important for me was the performance today,” Glasner said. "Especially in the first half, and let's say the last 20 or 25 minutes.
“It was a really fantastic performance with great power, really playing well, making pressure and always attacking the box, (playing) the ball in behind. I think the second goal was like this with Dani Munoz, with Daichi (Kamada)’s ball.
“This was the plan. We knew that they are very, very compact, but then also we were really going in behind and creating so many chances. It was really great to see.
“But on the other side, we also have seen, I think for maybe the 15 or 20 minutes after half-time, how good Fiorentina is in this situation, and we needed the crossbar and Dean Henderson once.
"Fiorentina started more aggressively in the second half. We lost the ball too quickly. But overall, the energy today here at Selhurst, with our fans, from the team, was great. I'm really pleased with what I have seen today.
“The first step is made, but we have to make the second in Florence next week.”
He added: "We also have to respect playing a very good team from Italy, that they would have maybe 15 minutes the momentum on their side.
“But we didn't get frustrated. We kept our heads up and knew that we could turn the momentum again, and so that's what we did.
“At the end, I think we were close to scoring the fourth goal – and it was a great performance.”