The Eagles controlled possession for large periods of the contest and went ahead when Ismaila Sarr struck two minutes before half-time after good work from Jørgen Strand Larsen.
But Zrinjski's Karlo Abramovic fired home a second-half equaliser following a smart breakaway, to leave the tie evenly poised ahead of next week's return game at Selhurst Park.
Glasner admitted Palace didn't do enough in the second-half to see the game out, but is confident his team can still progress in the second leg.
"We expected a very difficult game," he said. "Which is what we expected. It seemed like a very good start into the game, but then we lost a little bit of the directness towards the [their] goal.
"We controlled it, but were not really dangerous. We took the lead before half-time.
"But then, as I said before the game, we are missing consistency over 95 minutes and it was the same today. We were controlling the game then make an easy mistake.
"Zrinjski scored and then it's football...so they get the belief back, the crowd was back and it was tough.
"We were a little bit unlucky, but on the other side we were vulnerable in transition, in two or three situations. They did that well.
"So it's half-time and now we have to sort it at home, at Selhurst."
