Daniel Munoz struck in the first-half for the only goal of the game at Turf Moor.
“A very important win, a huge win, to be honest,” Glasner told Palace TV afterwards.
“For me there were more or less two parts of the game: the first 60 minutes we did well, controlled the game, scoring a nice goal, having the big opportunity straight after half-time, and the last 30 minutes it was then to survive and get the win over the goal line, and we did it.
“The players showed great resilience, we had fantastic support from our fans, and then together we could get this win, a very important win here at Burnley.
“I trust this group of players 100 percent, that they are leaving their heart on the pitch and giving everything they have. Even today, they wanted to play better in the last 30 minutes, but it just didn't work, and then we have to accept it and we have to support it.
“I think, right at the moment we can't expect that we're always playing brilliantly in everything, one-touch football, and it's easy. Then, you have some games on Wednesday evening, an away game, third game in five days, third time we're leading 1-0 at half-time – the last two we lost with set-play goals, it's somewhere in the back of your mind – and then being that resilient really makes you proud and just shows how great this group is.
“An important win, and 23 points after 14 rounds. I’m really proud of the team.”