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Good players will definitely be missed by their erstwhile club, but if the team is made up of quality players, their absence will not be felt that much or for a long period of time. Liverpool didn't have a bad season because of Sadio Mane's exit, they had a terrible season because most of their players were in horrendous form and the manager wasn't able to bring the best out of them. I think clubs should always allow their players leave if they say they want to, a football club should not be built around a few players but the entire team.
You are right, Liverpool are in a bad form not because of Mane leaving, but most of their players are not at their best. After all, several important Liverpool players also suffered injuries which ultimately affected the team's performance, and those are some of the reasons why they didn't perform well last season. The adaptation of some of their new players has not gone smoothly, it has also made Liverpool difficult throughout last season.
I believe Liverpool will get a better performance next season because they will only focus on the Premier League. Klopp will try his best to build on the quality of his team that fell last season, so that next season's Premier League competition will be even hotter.