Harry Wilson had canceled out Palace's opener struck by Eddie Nketiah before Marc Guehi scored the winner on 87 minutes.
"It's a great win here," Glasner told Palace TV. "Of course it was a tight game.
"What makes me really proud is that, although we were lucky in one situation when their goal was ruled out. But for me, the longer the game went on, the more likely it felt like we were to win it.
"We were playing forward, creating some nice attacks and creating chances – then we get the game winner from a set-play.
"A huge credit to the players and thank you to our fans who pushed us and supported us right until the end, we kept going.
"That's why I think, at the end, we deserve to win."
Palace currently sit fourth on the Premier League table and Glasner added: "It's a great picture. But for me, honestly, it's not really important. For me, it's the way we are playing, the commitment and always believing that we can get the win.
"I think this is much more important. You can lose a game and drop five positions. But yes, being more towards the top of the table, than at the bottom, it makes life a little bit easier and a little bit more relaxing.
"We are enjoying it, we are enjoying ourselves. This is what we want and what we have to continue to be successful until the end of the season."