The Saints had been walloped 6-1 on home turf in the same competition by Klopp's men last season, but they kept the Reds' thrilling attack at bay for a second time this season to take a 1-0 lead to Anfield in two weeks in the second leg.
Redmond had three other clear chances to put the hosts in greater control of the tie, and Klopp lamented his team's decision-making as another dim performance came on the back of the weekend's FA Cup stalemate against Plymouth Argyle.
"The start was like we are usually, but after that goal we conceded the reaction was not good," Klopp told Sky Sports.
"We lost timing, we were not compact enough. Nearly everything changed and it was not good.
"It's maybe easy to explain. We made wrong decisions, we can do much better.
"It's a cup game and in an away game, if you concede a goal, it's no problem but you must react.
"The first 20 minutes showed we are on the right path, open games are difficult, they had the biggest chances because we were not compact, [goalkeeper] Loris [Karius] had to save our life a few times.
"It's a deserved win for Southampton, but only half-time, so all good."
Philippe Coutinho was a buzzing presence on his first outing for almost two months from the bench, but the Brazilian appeared short of the sharpness required to turn the game around.
Asked if he had come through his half-hour cameo unscathed, Klopp added: "All good, good to have him back.
"You could see immediately in the few moments how important he is for us."