The Seagulls failed to progress to the competition’s semi-final, losing to the Reds on penalties after both teams were tied 0-0 following 120 minutes.
Despite the disappointment, he revealed that his team must respond and aim for a positive result against Aston Villa on Wednesday.
"I didn’t think we did enough in 90 minutes to win the game but in extra time we did, we had some big chances. I don’t know how well prepared their goalkeeper was but in the end he made two saves in the penalties so he was their matchwinner,” Hurzeler told Brighton website.
"In the penalties I wanted the players to focus on their job and what corner to go for. I chose them, they didn’t volunteer.
"We were not on our highest level in the 90 minutes. We weren’t intense or resilient enough so we weren’t able to play at our highest level but then in extra time I thought we improved but it wasn't enough.
"We’re disappointed but the main things now is to show a reaction, recover good and focus on the next challenge on Wednesday against Aston Villa."