The Reds dumped the Audi Cup hosts out of the pre-season tournament thanks to goals from Sadio Mane, Mohamed Salah and Daniel Sturridge.
The Bundesliga giants barely troubled the red-hot Reds defence in the sweltering heat of a Munich summer.
But Kop boss Klopp was not about to wax lyrical about the performance.
“We won 3-0 but I don’t like running around saying, ‘how good was this?’ because it wasn’t,” he said.
“In a few parts of course it was good, in a few other parts everyone saw that Bayern had the ball too often and it was too easy to play through our lines. I cannot ignore this on a day like today.
“Yes it looks good but they need to get fit and stay fit and hard and resistant because the season will be difficult. That is what we are preparing.
“I have to speak to things that are not good because I see it. I only say it us but I say it now because you asked the question.
“And it is not that I am trying to make the league afraid, ‘oh my god Liverpool beat Bayern 3-0 and they can do better.’ We have to do better and that is what we are working on.”
It was a message to everyone that he believes they can do better, but also appeared to be a clever ploy to stop his players getting ahead of themselves.
Klopp, of course, will want his players walking confidently into the new season when they travel to Watford on August 12.
But he will not want them overly cocky believing they are already good enough to blast everyone away in the Premier League.
The Liverpool manager will also have looked at Bayern’s pre-season which has included defeats by AC and Inter Milan as well as Arsenal.
Carlo Ancelotti is also clearly still figuring out how to include James Rodriguez into this team while the early injury to Thiago did not help much either.
Klopp did not use the usual caveat to every good result at this time of year which is ‘it’s only pre-season’.
But he flipped it to inspire his side to improve further and it will be interesting to see if they can go up another level.
