Eddie Nketiah struck a first goal for Palace, with Ebere Eze proving the matchwinner against his former club.
Glasner later said: “It was a tough game, but we expected a tough game here against a good Championship team in their stadium.
“It was very tight and then I think we controlled the game, took the lead, fully deserved. Then, they came back with a set play and the crowd got loud, and I think we had a great reaction. We scored immediately our second goal and, with also great support from our fans here behind the goal, over 90 minutes I think it's deserved – but it was a tough game.
“I think we have to accept that not every game is brilliant, when you play every third day and with a very, very big comeback against Leicester.
"With a lot of effort and then playing three days later here, and them getting the equaliser after a corner ,and then coming back... again, we're on the right pathway. It's not everything perfect.
“Sometimes you have to work for the win. We worked today for the win, and so we are pleased that we're in the next round.”