Diogo Jota struck early as the Reds won 1-0 in London.
Glasner later said: “I think we deserved more at the end.
“In the first half we could see how good Liverpool are, how quickly they moved the ball.
“We had a great start with the offside goal, and then we had problems and they had the lead. They deserved the lead at half-time.
"But the second-half gives me a lot of confidence for the rest of the season.We created chances and also we were good in defending.
“I think we must get a clear penalty for us. Marc (Guéhi) is held with two hands, but we have to accept it.
“The second-half performance for me was the best in the season and this gives me confidence."
Glasner also told Palace TV: “Of course, we're playing for results and it was a disappointment.
“But I also told the players right after the game that we will build up on this.
“I experienced in my career 1-0 down, and Liverpool playing like they did in the first half, that you leave the pitch with a 3, 4 or even a 5-0.
“But we came back and we came close to the draw. We didn't get it.
“It's tough, but at the moment it looks like we invest, we fail. We invest, we fail. We invest, we fail. The only way to get the turnaround is invest, invest, stay together and work.
“This is what we will do. Then we will get the turnaround. Then we will get the wins because we have the quality, we have the working mentality, we have the togetherness.
“This, again, gives me a lot of confidence.”