Rodgers was also keen to point out that rival fans only single out good players for stick after the Uruguay international found himself being jeered and booed by the crowd during this week's Olympic Games defeat to Great Britain at the Millennium Stadium.
"The first point is that opposition fans only give people stick because they're good players - you don't see bad ones getting it," Rodgers was quoted as saying in several newspapers.
Suarez was handed an eight-game suspension and a £40,000 fine in December after being found guilty of racially abusing Manchester United defender Patrice Evra in a Premier League match at Anfield. The controversy was re-ignited in February when Suarez seemingly refused Evra's handshake as the teams conducted their traditional pre-match greeting in the return meeting at Old Trafford.
Suarez then reopened old wounds during an interview with a Uruguayan television show last month, where he accused United of having too much power and blamed Evra for the failure to shake hands.
Rodgers continued: "Luis probably still feels a little bit of injustice about last season, but for me the message is that we have to move on. We have to move forward. What's happened has happened and let's let it go now, however hard it is. We want to be winning games and doing our best for the football club."
Suarez saw his participation in the Olympics come to an end with the defeat to Team GB as the highly-fancied Uruguayans were dumped out. Rodgers is now looking forward to welcoming him back into the fold after the Reds' season began with Thursday's 1-0 win over Belarus' FC Gomel in the first leg of their Europa League third qualifying round clash.
"It will be fantastic to have Luis coming back, and he is already fighting fit," said Rodgers. "He will have a couple of days off and join up with us after the weekend. He's been playing games, so he will already be up to a decent level of fitness, maybe even higher really, because he's had more competitive games. I'm really looking forward to working with him."
Regarding further additions to his squad, Rodgers said: "There is nothing imminent just yet, but hopefully things will progress over the next couple of days. It may take one or two moves to spark everything off. I want players in sooner rather than later, it is important to get the group together as quickly as possible, but if not we will just have to be patient.
"I have also looked at one or two loan deals from abroad. There are some quality players in that market that I have inquired about. The make-up of the group will change before the season starts and that will change the dynamic of the team also."