However, they have never before been victorious in each of their first seven matches in all competitions from the beginning of a new season.
Klopp brought on James Milner at the break as Liverpool eased to victory to maintain their flawless Premier League record and he explained his choice in a post-match news conference.
And Klopp was happy to welcome another unexpected milestone on his team's journey.
"I lost seven games in a row once, that felt different", Klopp, who watched his side reclaim top spot in the Premier League, said. "But then we won the eighth game 5-0, very cool!"
'All the different challenges with the different styles of the opponent, the boys were there.
Liverpool boss Jurgen Klopp admits his team has surprised him after their 3-0 win against Southampton.
Salah netted a staggering 44 goals in his first season at Anfield following his transfer from AS Roma last summer.
But his wait for a goal after a three-game drought was soon over when Shaqiri's wonderful 25 yard free-kick hit the crossbar and Salah grabbed his third goal of the season as it sat up invitingly on the line. He's uncomfortable but I don't think it's much more.
Marco Silva unhappy at 'clear offside goal' as Everton lose at Arsenal
The Gabon worldwide also saluted Gunners goalkeeper Petr Cech's display, and stated his belief that his team were on the rise. The Turkey global is still looking for his first goal of the season.
The Swiss worldwide understood the decision, according to his manager.
"That's how it was at half time, but he's a fantastic boy so there was no problem. He was not injured", said Klopp.
The Swiss worldwide took just 10 minutes to make an impact, although he was helped by some good fortune as he broke the deadlock. He was always a target to pass back to and was still involved in the defensive organization as you could see him communicating with the back line frequently.
Klopp allayed injury fears over Virgil van Dijk after the centre-back was taken off with a rib problem just before the hour mark.
"It should not be too serious". He said he couldn't shout any more, so that's obviously 60 per cent less of his level.
Klopp's side are yet to concede at Anfield in the league and Matip insists Liverpool's home ground has become something of a fortress.
The Reds have now scored each of the past 23 league goals recorded at Anfield.
"In the end we take a little bit of comfort from the second half performance in terms of not going under but clearly the damage was done in the first half".
The victory ended a positive week for Liverpool with a third win after a statement victory against top-four rivals Spurs at Wembley last weekend and the breathless, late victory against Paris Saint-Germain in the Champions League.