The Reds boss was furious with a number of decisions in their 2-1 defeat at Manchester City, most notably the one which saw Raheem Sterling flagged offside when he was at least two yards behind last defender Aleksandar Kolarov before racing through to beat Joe Hart.
Rodgers said the officials' performance was "horrendous" and then questioned whether it was right a referee from Bolton - barely 14 miles from Manchester - should have been in charge of the game.
"I was surprised we are playing in Manchester and have a referee from Greater Manchester," he said.
"I am sure we won't get (for) Liverpool-Man City someone from the Wirral.
"I thought they were horrendous in terms of performance.
"Hopefully we don't have another Greater Manchester referee again on a Liverpool-Manchester game."
Rodgers did not restrict himself to criticising the appointment of referees from the locality, however. He was most unhappy with the job they did over the 90 minutes.
"The officials make mistakes, I just felt the mistakes made shouldn't have happened at this level. This is a big game," he added.
"It was a poor decision and of course Raheem goes through and scores.
"I thought we never got any decision. The linesman on the offside one - he wasn't even on the same cut of grass.
"If you're working at this level you have to get it right. It's not even a difficult one.
"It is a perfectly-timed run and he is given offside when he is through one-on-one on goal. These are big moments in big games.
"There is another incident when Luis (Suarez) doesn't get a free-kick when Joleon Lescott went right through him.
"It is arguable it is a penalty at the end. Luis Suarez can't jump because he (Lescott) is tugging at his shirt."
Rodgers felt his players deserved more from the game having taken the lead through Philippe Coutinho only for Vincent Kompany and Alvaro Negredo to turn things around for City later in the first half.
"They were outstanding and really took the game to a top side full of top European players," he said.
"We are disappointed not to have won the game never mind losing the game.
"We showed great confidence and belief, scored a wonderful goal and could have had a few more but there are things to learn from the goals we conceded.
"We didn't get the points but we will recover well and get on to the next game (at Chelsea on Sunday).
"We have lost the game but we take a great deal of encouragement from it."