The Tykes lost 4-1, but Hourihane was pleased with the spirit his players showed, with Adam Phillips scoring before halftime after Dominik Szoboszlai fluffed a backheel inside Liverpool's penalty area.
The manager said afterwards: "I'm unbelievably proud of the lads, I thought they were outstanding. They stuck with the plan from minute one until the very end. We got a bit tired towards the end, as you can imagine, because we've gone so long without the ball at times.
"I thought we started the game so, so well. We stuck in there at 2-1. They are bringing on top player after top player and that was probably their best team out towards the end because they were making sure that they got over the line themselves., and I thought my lads were unbelievable.
"We had chances ourselves. We got the goal to get back in it art 2-1. I'm a little bit disappointed at our goal really because I don't think the player does that against Chelsea or Arsenal or in a Champions League game, so I was a little bit disappointed with that if I'm honest.
"I wanted the lads to put in a performance that they could come away from and be immensely proud of and they can certainly do that.
On if Szoboszlai's error was disrespectful, he added: "Yeah potentially. I don't think he does that in a Premier League game against Arsenal, Chelsea, Man City or in a Champions League game. I was a little bit disappointed with that."
Asked about what the goal meant to Phillips, Hourihane said: "Amazing for him. He grew up as a fan, came through the academy and went on a pre-season tour with Liverpool in the early day of his career. I'm delighted for him. He'll hold onto that moment in front of the kop dearly for a long, long time."