Suarez put in a dazzling performance at Norwich yesterday, scoring three goals and setting up another in the Reds' 5-2 win at Carrow Road. But one thing tarnished the Northern Irishman's first victory - yet another refusal by the match officials to award Liverpool a penalty after a foul on Suarez.
Leon Barnett clearly barged Suarez over and brought his elbow down on the forward's shoulder in the box, but referee Mike Jones did not give the spot-kick despite strong protests from the away players.
Last week Suarez was denied a penalty despite being fouled by Jonny Evans and the week before he received a yellow card for simulation against Sunderland, although replays confirmed the penalty shout was legitimate.
Some players in the Barclays Premier League have struggled to shake off their reputation for being a diver and Rodgers thinks the same may now happen to Suarez.
"There is that fear," Rodgers said.
"I could tell you about three or four strikers who go down in the box with very minimal contact, and all of them have had penalties this year.
"Everyone in the ground saw it was a penalty. Apart from the referee."
Rodgers' frustration with officiating in Liverpool's games so far this season came to a head earlier this week when he called referees' chief Mike Riley to complain his team were not getting enough correct decisions.
He insists he cannot ponder on the matter for too long, however.
He added: "I can't worry too much about it. It's something that hopefully the referees, when they analyse and assess their own performance, will have a look at.
"We just have to concentrate on building our game, developing our football, and hopefully these penalties that we don't get won't come back to haunt us."
Liverpool's failure to sign a replacement for Andy Carroll on transfer deadline day had left Rodgers worried that he would not have enough firepower for the campaign ahead.
Suarez went some way to allaying those fears yesterday by scoring three sublime goals and setting up Nuri Sahin for Liverpool's third.
The Uruguayan put Liverpool ahead after just 67 seconds and embarrassed Michael Turner by pinching the ball off the Norwich defender and then nutmegging him before beating John Ruddy to make it 2-0.
Suarez selflessly squared to Sahin for Liverpool's third and curled home a 20-yard strike in the second half to leave Rodgers purring with admiration well before Steven Gerrard added the Reds' final goal.
"Luis is a complete footballer," Rodgers said.
"He's not just a number nine box player who stands up there and waits for the ball.
"He has more tactical understanding of the game. He is clever in his technique... he moves well in and around defenders.
"All three were wonderful goals."
Unlike Liverpool, Norwich never looked like ending their winless streak yesterday.
With Grant Holt on the bench, the Canaries lacked penetration up front and they dearly missed the composure of Sebastien Bassong in defence.
First goals of the season for Steve Morison and Holt were the only positives for the Norfolk club, who now have the daunting task of facing Chelsea and Arsenal in their next two games.
Norwich performed better after their 5-0 hammering of Fulham on the opening day of the season and defender Russell Martin thinks yesterday's defeat was not a true reflection of the talents at Chris Hughton's disposal.
"The real Norwich is what you saw in the last three or four weeks - not what you saw against Liverpool," Martin said.
"We are deflated at the moment, but we have a work ethic in that dressing room that has got us to where we are over the last few years and it remains the same."
Some Norwich fans left after Liverpool's third goal went in even though the match was just 56 minutes old and they also booed their team off at half-time and after the final whistle.
"The fans pay good money and they have been unbelievable for the last few years so if they want to air their views then that's fine," Martin said.