Oh definitely, I can imagine Allen and Lallana were both Rodgers' signings.
However, both of them have arguably contributed much more than the likes of Mario, Markovic, Aspas, Ilori etc. who were more than likely not his signings.
Liverpool are a feeder club for big clubs, they'll sign a player and he'll perform well and then move onto a big team (Torres, Sterling, Suarez). They'll then use the money of the big sale to fund new players to try and turn into a saleable asset. Until they stop this cycle, they'll never compete.
Other than Countinho, I don't think they have any decent players anymore - which will be a big problem moving forward.
whats apparently been the system according to Tony Barrett of the times is its been kind of a trade off system, the other members of the transfer committee get him to take Mario, Markovic, Firmino who he doesn't really want but he gets his guys who they don't really want like Benteke etc and it really looks like a horrible way to run your club