No he should get two seasons (minus 8 games) before fans and owners should make a proper judgement. At this stage in Brendan's tenure we were on the verge of Liverpool's greatest every accomplishment in the Premier League era so obviously Brendan would get more time after this.
No we weren't, Rodgers' first season at LFC was pretty poor and only picked up after the January transfer window when Sturridge and Coutinho were recruited. We finished 7th if I remember correctly and were knocked out of the FA Cup by Oldham and the League Cup at home to Swansea.
He also inherited a squad which included Reina, Agger, Gerrard and Suarez, Klopp has inherited Mignolet, Lovren, Lallana and Benteke.
The above are facts, the club was in a much better position when Rodgers took over than it was when Klopp took over despite £300mil investment.