The controversial forward has completed a £75 million move to Camp Nou although he cannot feature for his new club until October as he remains banned from all football activity for four months after biting Giorgio Chiellini during his nation's clash with Italy at the World Cup.
Rodgers insists that Suarez did do badly by the club but backs the Reds to move forward without last season’s top scorer.
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"Of course there have been issues but they're in the past. He was a brilliant player for us and for me and I will always see him as a good man and a good friend.
"It's a shame he's not here but Liverpool, as a club, is bigger than any individual and we will move forward without him.
"It's really exciting going into this season. We've qualified for the Champions League and brought in some good players. Hopefully we'll progress."
The Liverpool manager also discussed captain Steven Gerrard's decision to retire from international football, which he feels will benefit the Reds.
"I've spent a lot of time speaking with Steven and I know how much it means to him to play for and captain England - he was a wonderful captain," Rodgers added.
"But Liverpool means everything to him and there's certainly no doubt missing out on international football means he will be fresher and at his optimum level as often as possible for us."