Despite holding a one-goal advantage going into the last 12 minutes of normal time, Palace had to survive a dramatic ending to the game.
The Eagles lost both substitute Eddie Nketiah and captain Marc Guéhi to red cards, before having to survive a huge amount of injury time - more than the 12 minutes that were originally indicated. This was partially due to Brighton also having a man sent off in the closing stages, when Jan Paul van Hecke was shown a red card for hauling down Daichi Kamada.
But despite the chaotic finish, Glasner refused to panic and was always confident his team could see out the job, even in the most trying of circumstances.
"We just showed them which system they need to play," he explained to PalaceTV. "And they knew what to do. One or two situations changed, with Daichi [Kamada] as like a left wing-back.
"It was not so difficult because we often train nine vs ten, sometimes eight against ten - but not so often!
"But the players know what they have to do. What I really loved today is that they didn't just defend and wait for the referee to end the game.
"We were waiting for the right moment to go forward, with Daichi forcing the red card, otherwise he would have been one-on-one with the goalkeeper. This mindset I really loved today."