All in all, it was game of positives for Liverpool as they calmly won their sixth consecutive game in a row in the Premier League and seven in a row across all competitions.
When quizzed about van Dijk's injury, Klopp said: "He already had a bruise in the ribs before the PSG game, which is very uncomfortable and today he got another hit there". Yes, it's a surprise because of course you can not expect it, but all performances we showed so far were at least good enough to win the games.
"He tried everything. We only had problem in defensive [situations], offensive it was a good idea".
Southampton responded reasonably well as Jannik Vestergaard went close from a corner, and Virgil van Dijk, playing against his former club, had to be expertly positioned to ensure that Shane Long did not make the most of some good crosses into the box.
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"All the different challenges with the different styles of the opponent, the boys were there".
Speaking at a news conference before Liverpool FC's clash with Southampton on Saturday, Reds boss Klopp said: "He had fantastic offensive situations in both of the last games".
'I said to Shaq that I have never taken a player off at half-time after such an influential half but we wanted more control.
With Chelsea and City to come in their next two league games and a Champions League visit to Napoli in between, Liverpool understandably took their foot off the gas in the second-half. It will be tough, but for all of us, so that's absolutely OK.
Although Liverpool dominated the game in its entirety, they made it hard for themselves in order to get full points from that game.