Palace went ahead through Ismaila Sarr just before half-time. Zrinjski's Karlo Abramovic fired home a second-half equaliser following a smart breakaway. Palace will host the second-leg of their Europa Conference League playoff next week.
"We expected a very difficult game," Glasner 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 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."