Paul Onuachu appeared to have secured Saints a 1-0 win before Matheus Franca headed home an injury-time equaliser for the visitors.
Glasner said afterwards: “I'm very pleased with the point today.
"I think we all know that we can play better, but today it was really about never losing the belief and to keep going until the final whistle, and this is what the players did.
“We were missing a few percentage in every phase of the game and we looked a little bit mentally tired, not at our top. Then also missing the first chance, then being down 1-0. We could see the players at half-time.
“We encouraged them and said, ‘yeah, sometimes it's a game where you don't perform at your best, and then it's never lose your belief, always keep going, because we will get one, two or three chances’.
“This is what I really appreciated today and what I'm really proud of: that this group always sticks together. We had a great impact from the players, from the subs today, also for pushing and getting this well-deserved equaliser. Even then we went for the win and had a big chance with Eddie (Nketiah).
“The second thing today, I think, all Crystal Palace staff and fans can learn is to stay humble, that we can't take it for granted, going everywhere in England and going home with three points. Every point is a good point and today, for me personally, it's a very good point.”
On goalscorer Franca, Glasner also said: “I'm always talking about it before a game and after the game, that we can just be successful as a team. We need every single player, so it's good to have them available.
"Joel Ward was back for the first time in the squad, and also Matheus França – for him, personally, it’s a great night. He was scoring his first goal for Palace after a 10-month injury, then he had a birthday this week and he became a father two weeks ago.
“He gets now a lot of great things back for all his investment in a tough, injured time, and it helped us today to get this point.
“I always hope and wish every single player to score a goal, because I know this is why we are playing football. Of course, for him, with his personal story, it's great and it will help him, and it will help us.
“It's good that we know we have more players who can score goals, because to win games you need to score. It will help him as a person, and it will help us, definitely.”