A 2-1 defeat in Florence against the Italian side on Thursday ensured that the Eagles qualified through to the final four with a 4-2 aggregate win, thanks to a 3-0 home leg win last week.
And for Glasner, who won the FA Cup and FA Community Shield last year with the club, just two games separate him from another final with the side from SE25.
Awaiting in just two weeks are Shakhtar Donetsk after the Ukrainian side booked their place against AZ Alkmaar.
“When you play in the semi-final, you want to get it all at the end and that’s what we will go for,” said Glasner after the game in Florence to TNT Sports.
“I actually played against them with Wolfsburg straight before COVID with the second leg six months later (the first leg in March, the second leg in August 2020).
“We lost and at the time, they had many Brazilian players too, so I expect them to be a very technical side.”
After a strong opening 20 minutes, which saw Ismaila Sarr head home from a Daniel Munoz cross and Palace create several opportunities, Glasner lost Maxence Lacroix and Adam Wharton before the half-time whistle due to injuries.
“Adam Wharton felt his adductor and that’s why he left the England camp a few weeks ago, so let’s see,” said Glasner in his post-match media conference.
“We have to do further assessments. Maxence Lacroix had a clash. The medial ligament in the knee is overstretched, hopefully it’s not too serious, but I can’t tell you the exact diagnosis.”
After Sarr’s opener, Fiorentina got back into the game on the half-hour mark, Albert Gudmundsson sending Dean Henderson the wrong way from the penalty spot.
Substitute Cher Ndour then made it 2-1 on the night and 4-2 overall, with just under 40 minutes to play, but Palace withstood the pressure with Fiorentina running out of steam as the visitors closed out the final 15 minutes with ease.
“A quarter-final is never easy, and we did it a little bit tougher than it could have been,” said Glasner.
“We had a great start into the game, taking the lead, but with the penalty Fiorentina got the belief back and then was really a very difficult game to manage.
“Quite early in the second half, all of a sudden, we were 2-1 down but the reaction was great again.
“We didn’t play really attacking football, but we defended very well and the team showed resilience. It was really being resilient and working hard, sticking together. It was a very intense game and we did what was necessary.
“Over the two games, we deserve to play in the semi-final. We’re celebrating to go to the semi-finals and it’s a massive achievement for the players and a massive achievement for Crystal Palace that we will enjoy tonight.”