Making his fifth successive appearance in the league, the goalkeeper played a pivotal role in the opening goal at St Mary’s.
It was Karius’ quick decision, having thwarted a Saints corner, to throw the ball forward for Alex Oxlade-Chamberlain to release Mohamed Salah – who promptly set up Roberto Firmino to net.
The German then denied the hosts with a series of saves, notably rushing from his line to block a close-range effort by Pierre-Emile Hojbjerg and then tipping over James Ward-Prowse’s header.
And the visitors capitalised on his stops to double their lead through Salah before half-time, which proved enough for three points that restored them to third in the Premier League.
“That’s my job, to try to be there for the team when needed. The first half was a bit busier than the second – but that’s my job,” Karius told Liverpoolfc.com.
“It was a very important game. We saw the other results, we saw Tottenham win – but we did our job. We kept a clean sheet and scored fantastic goals, that’s all we wanted.
“It’s good to go to the next away game with a positive result and to feel strong. We’ll recover and focus on Porto, which will be a big game for us.”
Watch: Karius' crucial first-half saves
Though Liverpool conceded twice against Tottenham in their previous outing, Karius made several impressive saves that afternoon too – including a penalty from Harry Kane.
The No.1 feels his form is founded on having a stable position in the team.
“It’s good and I feel good. Getting weekly game time is very important,” he said.
“I’m still young; I had plenty of experience in the past but it’s different if you play week in, week out again and not just come in every other week for a midweek game.
“My confidence is coming and growing, I’m getting used to the game time again. It’s good for me.”
As Karius denied Southampton at one end, Firmino and Salah combined to defeat them at the other.
The pair took turns apiece to create a goal for the other and thereby increase their season tallies to 20 and 29 in all competitions respectively.
“[They are] phenomenal, great guys,” added the ‘keeper.
“Everyone is working hard for them to score the goals at the end. They are brilliant players but it’s about teamwork and putting them in the position.
“We all know the quality they have, so if you keep a clean sheet then you pretty much always score with these guys and get three points. That’s what we have to focus on: defend and then they’ll do the job up front.”