Yes, it was the season before! Sterling and Suarez as well as Gerrard, all 3 had gone by the time Klopp arrived, and Sturridge was already going down the route of being injured constantly before he arrives. And Gomez also got a bad injury the week he arrived and he didn't get to use him till over a year later. Klopp didnt get to reinvest the money from the sales of Suarez or Sterling, they'd long gone. Rodgers had allready spent that money on players.
A lot of revisionism really in what you say, as the general concessus was that Lovren was awful, Henderson and Lallana where certainly not considered all that by opposing fans, Firmino had done nothing in his few months under Brendan Rogers, neither had Origi. When Rodgers was sacked, the view generally from opposition fans was that he had bought a lot of average players for a lot of money and Liverpool's squad wasn't very good. Ask yourself what players you would have wanted from that team he left? I'm pretty sure if we where being honest about the only name that would have come up was Coutinho.
But no he didn't start from scratch - not many a coach ever will, but he took on a team with a poor goalie and defence, a functional but pretty average midfield,, one genuine star player in Coutinho, and a striking duo of an injured Danny Ings and Christian Benteke. But he did improve players for sure, like Origi, even Lovren, of course Firmino too, a player he already knew all about and knew how to use him.