Palace booked their spot in the last four of the competition for the second time in four years, battering Fulham 3-0.
However, the Eagles were up against it in the first 30 minutes at Craven Cottage, facing a barrage of Fulham attacks, albeit the hosts could not take advantage of their dominance.
Completely against the run of play, Eberechi Eze produced a moment of magic in the 34th minute, receiving Tyrick Mitchell’s pass inside before blasting his effort into the bottom right corner.
Five minutes later, Eze’s impact again sent Palace into dreamland, with his cross headed past Bernd Leno by Ismaila Sarr.
Palace’s earlier discomfort very quickly turned into stability as they limited Fulham's chances and started to look brighter.
Eddie Nketiah, subbed on in the 70th minute, wrapped up Palace’s spot at Wembley five minutes later when he rolled his right-footed effort through Leno’s legs.
Getting a step closer to ending Palace’s 164-year wait for a trophy, Glasner believes it is a great moment to reach the semi-finals of the competition, but insists that his side has not achieved anything yet.
“The season is not over. If this is the end today, I wouldn't be happy. It is just the start of our crunch time of the last two months now.
“Hopefully, we have 12 more games to play. The good thing is we are in good momentum and the players are in good shape. The next two months we always stay together, we can train a lot and we have many games to get into our best shape again.
“I think today, especially at the beginning, we were far away from this. We need to perform at our best to win as many games as possible.
“I don't want to talk about winning a trophy because even in the next game we can’t win a trophy. It is just the semi-finals. When you enter a cup competition it doesn't matter if you lose in round number one or the semi-finals. We entered the competition to win it.
“It is a great achievement to play the semi-final and especially in that environment at Wembley as it is always something special with both semi-finals played in the final stadium. That is something typical of English and I really like it.
“In the end, it is about being ready in four weeks to win this game. It’s not that we have four weeks to prepare for this game, tomorrow we will start preparing for Southampton. In the league, we have the chance and opportunity to enter the top half, we keep going.”
Glasner, 50, has never competed at Wembley as a player or a manager, with next month's trip to the home of football marking a personal milestone for the coach in his first full season as Palace boss.
After the win at Fulham, he told the media about his previous encounters at Wembley, including the spirit of walking along Wembley Way.
"I visited Wembley for England against Belgium last year. The second time I went to drop my daughter off at a Taylor Swift concert – I saw all the young fans and thought I was too old for this.
"I was there on Monday to watch England versus Latvia and see our players. I’ve been there three times, but I’ve always been by tube. I really enjoyed Wembley Way when you can see the arch in the queue. That’s what I love."