The German manager watched on in fury as Saints centre-back Lyanco collided into Diogo Jota in the 13th minute of the first-half. Referee Martin Atkinson waved play on and Southampton capitalized, breaking forward with Nathan Redmond curling home a magnificent strike.
Klopp reacted with outrage at the opening goal, having deemed the challenge from Lyanco to have been a foul.
But Carragher has dismissed the Reds manager's reaction, telling Sky Sports (via Mirror):
“When I watched it in normal time it looked fine, I’m far away from it."
Martin Atkinson was close to the scene of the foul and Carragher touched on this, saying:
"I mentioned Jurgen Klopp was furious at the side of the pitch. Martin Atkinson was in a really good position."
The former Liverpool defender later on then reanalzyed the tackle stating:
"(Going) back to this foul that led to the goal and upset Jurgen Klopp. He’s (Lyanco) pointing at the ball. I think he possibly takes Jota just before he takes the ball."
Liverpool would eventually equalize through Takumi Minamino, with the Japenese midfielder sending a fine strike past Angus Gunn in the 27th minute.
Then in the second-half, Joel Matip headed home in the 67th minute to put his side 2-1 up.
Liverpool still on route towards an unprecedented quadruple
Jurgen Klopp's men have controlled large phases of the game and have performed admirably despite a host of changes made by Klopp.
Mohamed Salah, Sadio Mane and Virgil van Dijk have all been given a break and haven't even been named on the bench as Klopp made nine changes overall.
The likes of Curtis Jones, Harvey Elliot and Konstantinos Tsimikas have been afforded the opportunity to impress.
A win is a must given Manchester City's superior goal difference.
There is a seven-goal deficit for the Anfield side to make up if the Saints can find an equalizer and if City slip up on the final day of the season against Aston Villa.
The Reds are still eyeing an unprecedented quadruple, having already secured the Carabao Cup and FA Cup. They head to Paris on May 28 to face Real Madrid in the UEFA Champions League.
Klopp's decision to hand a number of his first-team regulars a rest speaks volumes of the depth of talent he has at his disposal.