The Reds dismantled Manchester City to find themselves 3-0 up just after the half hour mark in the contest as Klopp's men went on to win 4-1.
But Klopp seems to have identified that Liverpool need to replicate their away performances at home. Klopp's away record in all competitions currently reads three wins and a draw, while his home record is one win, two draws and a defeat as his side have failed to find their scoring touch in front of their own fans.
One challenge seems to be that Liverpool's more impressive performances at the moment seem to be coming on a bigger pitch at the likes of the Etihad Stadium, and despite the state of the playing surface, their Europa League win over Rubin Kazan.
Of course, away from home there is more emphasis on the home side to take the game to the visitors, which suited Liverpool on Saturday as they showed their strength on the counter attack. Whenever Manchester City conceded possession they were punished. At Anfield, teams are going to be more inclined to let Liverpool have the ball and try and break them down. Klopp himself has said he will find a solution ahead of the game with Swansea City on Sunday, though a win against Bordeaux three days earlier would be pretty good preparation as they seek to secure qualification from Group in the Europa League.
Therefore, there could be change in personnel at the top end of the field. Leaving Christian Benteke on the bench and leaving Roberto Firmino to lead the line has worked a treat against both Chelsea and Manchester City, with Benteke proving to have a telling impact in the former as the Reds threat changed somewhat.
The thing that Klopp has to his advantage here is that players are returning who can aid him in helping turn around stubborn defensive units. One example of those will be West Brom in just under three weeks; Tony Pulis loves nothing more than frustrating sides on their own patch and picking up a clean sheet for a good afternoon's work.
What Liverpool did so well against Manchester City was be able to get men beyond the defensive line and continuously turn them around, something which won't be so busy on a narrower playing surface against a side who is content with allowing the Reds to play in front of them.
As a result, having Daniel Sturridge fit and available going into this period could prove to be crucial in order to provide that clinical edge, Christian Benteke hitting his stride will be welcome, while Philippe Coutinho discovering his scoring touch is also a welcome boost in this area.
Of course, the defence has to do their bit as well. It's not going to be free scoring Liverpool all the time but if they want to generate the kind of performance at the Etihad on show at home then they need their defence not to overplay with the ball, and get it forward as quickly as possible rather than play themselves into danger. Cutting out others errors that have been prevalent in recent months would also help.
There is that bit more added pressure at Anfield, especially against sides they are expected to beat but that is something they are just going to have to handle. If they get into a habit of beating teams they should do, and comfortably, then it could well be a fortress again.