Alexander Isak and Andrew Robertson had Liverpool 2-0 ahead before Daniel Munoz pulled a goal back for Palace. Florian Wirtz eventually restored the two goal for Liverpool late on.
Glasner said afterwards: "The difference was the efficiency. Liverpool were clinical and we were not.
"The Liverpool goalkeeper (Freddie Woodman) had the day of his life so congratulations to him. We kept believing until the end. It was really positive and this is what we take into the final weeks.
"I told them that I think it was our best performance here against Liverpool. We were very competitive here today.
"I showed them the stats. We were 2-0 down at half-time, and you could say 'we rest our power for the Conference League semi-final' then maybe lose 4-0, or something, but we didn't.
"This performance will give us a lot of confidence for the rest of the season."