You shouldn't run into conclusions on which club will be in the finals. Liverpool is still hopeful than Arsenal, because Tottenham only scored one goal. If Liverpool can win with two goals ahead, they will definitely be in the finals because Tottenham is not consistent. Arsenal might not qualify to the finals, because they need three goals to be in the finals and Newcastle is consistent in their matches.
I am pretty sure that Liverpool just simply doesn't look like they care about the EFL cup at all. Maybe they will recover and do better but I am not so sure that they even want to. Remember, this team is also on FA cup and they are also in the League and they are also on UCL all at the same time, which shows how this could be a very tough deal for them and not really look like it would make sense.
This is why I believe we may see Liverpool just not play with 100% here. In any case, I disagree with the notion that Liverpool may have hit the truck like City, just because they had a few bad results back to back doesn't mean that they are going to keep doing worse, it is not really something we should be concerned with, they are still a good team and I still think they will win the EPL as well. That's the most important part, not sure how well they can do at UCL but I am sure that they are going to end up winning the premier league and that's all that matters.
Liverpool are in top form, which allows them to win all the trophies in every competition they participate in. Liverpool priority scale is clearly in the Premier League and Champions League, but they will not throw away their chances to win the Carabao Cup and FA Cup. Of the 6 matches in three different competitions that Liverpool have to face until the end of January, I think there is no team that really makes Arne Slot need to worry. Arne Slot only needs to adjust the tempo based on the intensity of the competition, because I think they are not under pressure.
Turning things around by chasing a one-goal margin is easy for them to do, so the chance of qualifying for the Carabao Cup final is still quite big. Liverpool are also not under pressure when playing in the FA Cup, because their next opponent is a mediocre club. Liverpool position in the Champions League is quite safe, and they can qualify for the last 16 comfortably. In the Premier League, Liverpool are leading the standings with a difference of 6 points from their closest rivals Arsenal, and they also still have one postponed match which allows the points difference to be even greater.