Klopp made nine changes to his line-up for the trip to St Mary's on Wednesday (AEST), where Liverpool realistically had to win to keep hopes of winning the Premier League title alive.
Although the Reds fell behind to Nathan Redmond's opener, Takumi Minamino pulled them level before half-time and Joel Matip's header secured a huge three points.
Minamino also scored in his most recent previous Premier League start for Liverpool – a 7-0 win over Crystal Palace in December 2020. That gap of 514 days between scoring in consecutive starts for a top-flight club is the longest since Duncan Ferguson's 533 days for Everton from April 2002 until September 2003.
Klopp was proud of the result and said any further success that Carabao Cup and FA Cup winner Liverpool experience this season is down to the strength in depth they possess.
"I'm so happy about the performance, it was a bit touching, to be honest," Klopp said.
"These boys, it's like having Ferraris in the garage. Harvey [Elliott], I'm not sure when he played last. Curtis [Jones], no rhythm, he played from time to time. Takumi Minamino, it's a crime he's not playing more often. Oxlade [Alex Oxlade-Chamberlain] didn't even play and he's in outstanding shape.
"It's really tough for the boys, but whatever happens this year happened because of this group. It's exceptional, and tonight they showed that again."
Klopp added to Sky Sports: "I've never had a group like this. Because we win most of the time there are not a lot of things you can really argue about. But there are two opportunities how you can deal with it: you give up, or you play your role in the group, and this group push each other constantly.
"In the end it's absolutely outstanding. We came here and had to do what we did, and it worked out because of the boys."
Joe Gomez hobbled off injured at half-time and did not return for the second half. Klopp was hopeful the defender had avoided a serious injury, though he reportedly left the stadium on crutches.
"I hope we are lucky. Joe himself has pain but not too much, but it was really like a shock to the system,” Klopp said.
“He was sitting in the dressing room, when I spoke to him he was in a good mood so I think we were probably lucky, but we have to figure that out."
Liverpool are one point behind leaders Manchester City, and will have to beat Wolves at Anfield on Sunday to stand any chance of winning the Premier League.
City will be entertaining Aston Villa at the same time, but Klopp is not planning to chat to Steven Gerrard before he takes his side to the Etihad Stadium.
"No, of course not … There's no reason to talk to him [Gerrard]. We all know Villa wants to win because Villa wants to win," said Klopp.
"We have to first win our game, we can't talk about Wolves as if they will not be there. It's difficult enough.
"Imagine we went there with one ear in Manchester and [Raul] Jimenez headed in the ball. We will be 100 per cent focused.
"So many things happened in this second half of the season. If we become champions it would be deserved as well, but for that we have to win."