Twice Palace fell behind in an absorbing 90 minutes, but twice Glasner's team were able to hit back to level, before a dramatic penalty shootout win.
Liverpool qualified as reigning Premier League champions and started fast, but the towards the end of the game, Palace looked more likely to grab the win in normal time.
After picking up the second trophy of the year, the manager told Palace TV: "We have showed that our confidence is high. We [last season] drew 2-2 at the Emirates, we won at Tottenham, we won at Manchester United. So I think we proved it many times that we have this belief and this confidence.
"But on the other side, it's always important to stay humble, it's just the start into the season, we also could see we have things to improve.
"We knew we would start on a different level than the year before, because we could keep the squad together, and the mindset, the belief, the togetherness is here.
"We could also see that maybe physically we are not at our top level, but you can't be in the first game. But what I I could see should give us confidence that we will play a good season.
"If we stay humble, if we keep working hard, these are the foundations where we build our game."
