Jürgen Klopp has demanded more from Sadio Mané and Mohamed Salah as he insisted Liverpool must improve before the new Premier League season.

Klopp’s team recorded an impressive 3-0 win at Bayern Munich on Tuesday when a front three of Mané, Roberto Firmino and Salah, supplied consistently by Philippe Coutinho, dismantled the German champions on the counterattack.

Despite the impact of Salah – Liverpool’s £36.9m record signing from Roma – and Mané’s recovery from knee surgery, Klopp believes they need to be fitter to sustain that form over the course of a Premier League campaign and that the team’s overall work must improve, too.

The Liverpool manager said: “Sadio is not where he can be so he needs playing time, playing time, playing time. We won 3-0 but I don’t like running around saying: ‘How good was this?’ because it wasn’t. 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.

“They [Mané and Salah] are both good but they don’t need to know it all the time when they play together, with Phil Coutinho behind as well to play all the passes for them to run in behind. Football is not that easy so I don’t want to talk about this. 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 about things that are not good because I see it.”

Klopp took more encouragement from Liverpool’s second-half display in possession than any individual contributions. “The beginning of the second half showed that in a game like this – and OK, 2-0 at half-time is a good result – we can be dominant with the ball against an opponent like Bayern. In that case we should do it, not wait until the second half or whatever.

“It is not that I am trying to make the league afraid and think: ‘Oh my God, Liverpool beat Bayern 3-0 and they can do better.’ No. We have to do better and that is what we are working on.”