Suarez or not, Rodgers deserved last season. Regrettably he made such poor use of it that, coupled with the fact that his own mistakes were part of the reason why we didn't win the title the previous season, I strongly suspect he'd have gone last summer if we'd been able to strike a deal with the likes of Klopp or Ancelotti.
Like others on here, I suspect the fact that we weren't able to reach agreement with someone of that stature is the only reason why Rodgers was kept on and why they backed him in the market. I don't totally blame them for the latter BTW - given that they weren't able to replace him as they (probably) wanted to, I expect they thought leaving him in charge of the same squad would see us drop like a stone down the league, and nobody could have foreseen quite how hopeless we'd look against West Ham (FFS) and how lacking in fight we'd be against the Mancs.
IMO none of that means we should now continue flogging a dead horse with Rodgers in charge. My hopes for him and for the club under him had been leaking away last season, the West Ham game was the final straw and yet another surrender against the Mancs underlined that for me. I happen to think he does have talent as a coach and may well do a good job at another, less pressurised club, but as far as Liverpool FC is concerned he has to go.