The Reds went into the game on the back of their Super Cup victory.
Klopp said, "We will never forget that for sure, our supporters will never forget that. Actually, it is easy to be happy after the game and then be concentrated the next morning about the next thing. It is not that we now run constantly through the floors or whatever and celebrate and don't put our arms down! It's all OK. That's why I liked it so much [today].
"We are not used to winning big things and then coming to Southampton, I really loved how much respect we showed today. I said before the game that this looks like the biggest banana skin in history; everybody is waiting for it and probably all the headlines were written already. I told the boys the headline I would prefer is 'the mentality giants were in town' – that's how I feel it in the moment. The boys did an outstanding job for today, all good, let's go home, recover and start again."