Liverpool experienced a decline in form because Mane left, as well as when Ronaldo left Manchester United to join Real Madrid.
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.
Is Mane an exceptional player, yes! Did Liverpool miss him, yes! Did liverpook fell off because of him, no but the absence was felt. We can't denied the fact that Mane played an important role in Liverpool forward last season, he was the best thing that happen to Klopp ever since he came into that club but then as you said, the rest of the players were in zombie mode as if they weren't doing anything at all but I doubt if Mane remains in Liverpool, the situation would have been better, no player that was signed could do the combined assist and goals he scored in a season was done by any of them, not even the old ones like Firminno nor Jota did what he did in his last season in Liverpool.
I will say that if Sadio Mané actually stayed in Liverpool, the situation could have been a little better. But there would’ve been a drop in performance still. Liverpool had a lot of problems in the last season. Not having Sadio Mané is not the only problem. Only one player cannot be so important for a team Should absolutely fail. There was very little chemistry between the players. And the team did not work as a whole. They will have to fix all the problems. They will have to compete for the English Premier League title next season. Sadio Mané is gone and he’s not coming back. They will have to accept it and move on.