Brighton stunned Manchester United with a 3-2 victory last weekend and pushed hard for an equaliser at Anfield on Saturday.
But Mohamed Salah's 23rd-minute strike following Yves Bissouma's error proved decisive, with Liverpool goalkeeper Alisson saving superbly from Pascal Gross late on.
"Yes, [a performance] to be proud of but we're disappointed as well because the form Liverpool are in you don't get many opportunities to get something from the game," Hughton told BT Sport.
"Over 90 minutes you know they'll have chances, we had chances as well. We finished strong and we won't have many better opportunities.
"At 1-0 down at half-time most people expected Liverpool to push on, but I thought we got stronger as the game went on.
"We were good on the ball, we had good moments. If we were more clinical we get something from the game."
Hughton added: "It's a poor goal, we try and move on from that as quickly as possible. The team rallied round because at that stage you can buckle under, but they didn't.
"You have to learn from it, but it is a soft goal."