The Seagulls suffered a 3-0 defeat at Liverpool in the fourth round.
Albion head coach Hurzeler said: “I think moments decided the game, unfortunately in the wrong direction.
“We started the game well, we controlled the game. We had a lot of good patterns.
“I think the goal from Liverpool came out of nowhere.
“We reacted well, we had two big chances where we have to score.
“I think in the second half the same, one big chance for Lewis, and then two, three minutes later, Liverpool scored with a great goal.
“These moments decided the game. I think that was a difference today.
“They had the quality to use their chances. We weren’t able to be that effective and therefore it’s a disappointing result for us.”
Albion took encouragement from their midweek performance at Aston Villa but this defeat felt more deflating.
Hurzeler said: “I think it’s very important to see the reality where we are at the moment, but it’s also very important to see the performances.
“The last two performances, and against two tough opponents, we were more than competitive.
“We were in both games there to take the game, I think in both games, the game could definitely also go in another direction and therefore we have to see the positives.
“We did a lot of things right but it’s very important to see also the reality where we are at the moment.
“We have to keep working harder. We are not in a good moment, so you only can come out if you show personality, if you keep sticking together. That’s what we will do.”