Palace reached the final for the first time in nine years as Ismaila Sarr's double and a rocket from Eberechi Eze sealed a 3-0 win against Aston Villa.
Glasner's side took the lead in the semi-final through Eze's long-range blast before Sarr netted twice in the second half.
In the final on May 17th, Palace will face Nottingham Forest or Manchester City, who meet in the second semi-final on Sunday.
The Eagles have never won the FA Cup, losing their two final appearances against Manchester United in 2016 and 1990.
"All the credit to the players. They had to work so hard. They had to overcome a few difficult moments," Glasner said.
"We got more control and it was an unbelievable performance. The players stuck to the plan and we never lost our heads.
"I don't know at the moment how I feel - a bit exhausted. The players have four days off now. They should enjoy the moment."
Villa, who last won the FA Cup in 1957, were hoping to make the final for the first time since 2015.
But Unai Emery's team produced a dismal display and will have to settle for fighting to qualify for the Champions League via a top five finish in the Premier League.
"When they scored the first goal it was more difficult for us and we only reacted after 2-0 and then we created more chances to score and we didn't do. In transition they are very good, and they deserve to win," Emery said.
"Sorry to our supporters because they were motivated. We have to accept it. We have to be quick to react because in the league we have the most important objective."