Liverpool entered the tie, having drawn the initial match 2-2, following a comprehensive 3-0 Premier League defeat at Brighton & Hove Albion. Harvey Elliott's fine 13th-minute strike settled the tie to keep Liverpool's FA Cup title defence alive. Incidentally, the Reds face Brighton at the Amex Stadium in the fourth round later this month.
"I think everybody who is with us got that reaction; it was the reaction we needed to show," Liverpool manager Klopp said. "We were compact, we were together, we had really good challenges, won challenges when we lost the ball and we played really good football in moments."
A sublime strike from Elliott, who collected the ball inside his own half and drove up the pitch before unleashing a looping, long-range effort beyond goalkeeper Jose Sa, proved the difference and Klopp was unsurprisingly impressed with the match-winning goal.
"We scored an exceptional goal where Harvey saw something that I think not a lot of people in the stadium would have seen," he said. "If I was a goalie, I wouldn’t have expected a shot in that moment.
"It was a top goal, but apart from that the game was much better, completely different to the last one obviously and I am really happy with that," Klopp added. "All the individual performances were good and we were really together wherever we were.
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"We won the ball higher up the pitch, we won it in the midfield and it was good. I said to the boys after the game that’s how it feels when you play well and win. We can't remember it really anymore when that was the case, but tonight it was the case and we are quite happy."
Teenage midfielder Stefan Bajcetic made his first start for Liverpool, and Klopp was pleased with the 18-year-old's display.
"Good player, very smart in his movements," he said. "Especially the younger you are, the more important it is that you have a good start in the game. He had a few situations where I am not sure he saw there was space or he just hoped there was space when he turned – and there was actually space.
"He did really well, but what helps really is that he wins these challenges. The last few steps before he has to block the ball, that's really good."
Klopp said he had no concerns about facing Brighton again, so soon after the heavy league defeat which dealt a fresh setback to Liverpool's hopes of finishing in the top four and qualifying for next season's Champions League.
"No problem. We come to Wolves again pretty quickly as well. That's football, no problem," he said. "We wanted to go to the next round and we knew already Brighton were the opponent, so no problem."