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.