Whilst the German was undeniably pleased with the result, he also stressed the need for his side to improve at the back.
In an interview with 'Sky sports' after the game Klopp said: "Two games, two wins so that's of course the best thing. You can see it was difficult again and it was not 100 per cent of our physical ability."
"Players like Riyad Mahrez and Jamie Vardy, they cause you problems so we're a little bit too late in the mind because the legs are tired."
"I thought we could have defended the first goal seven times already, but in the end it is a cross and a free header so it's not nice but it's what happens. We came back and even before the good goal, we were already the dominant side and playing good football so it was all OK."
"I liked everything I saw but that [defensive work] is something we need to fix 100 per cent. I know it is pre-season and we can change it but it is something I don't like already so we need to work on it."
The former Borussia Dortmund boss also rubbished reports linking Coutinho with a move to Barcelona.
"There is no doubt about these things [Coutinho's commitment to Liverpool], so why should he prove it then? He is a fantastic footballer and a fantastic boy," Klopp stated.
"He had a few wonderful moments offensively but we have to stabilise ourselves in defensive situations. Like I've said, you can't train for being a real challenger and a real defender in these moments."
Overall Klopp was happy with the trip Easy, saying: "I'm happy that we came here now, we had a few moments which really made us stronger as a team and I'm completely fine with it."
"Everything can be improved although what we have done so far is completely OK."
With time ticking inextricably away before the start of the new Premier League season the 50-year-old will be keen to get back to work to iron out the kinks in his team's play as they look to mount a serious Premier League title challenge this time around.