The Anfield boss saw his side get their Premier League campaign up and running on Saturday with a 1-0 victory over Stoke City.
Striker Suarez was in attendance as a Daniel Sturridge goal gave the club their first opening-day win since 2008 - despite being banned for the encounter as he serves the remainder of his 10-match suspension for biting Chelsea defender Branislav Ivanovic.
His appearance in front of the Anfield crowd came just a day after returning to training, with the 26-year-old having been exiled from the first-team squad following his public outbursts over his desire to leave the club.
And while he refused to be drawn on whether the striker had made an apology, after the match Rodgers did attempt to draw a line under the affair.
"The concentration is on the players who are available to play," Rodgers said. "Luis is doing his work, there is nothing to be said there.
"I'm very satisfied with how everything has been resolved, as a club we are looking to the future and moving on."
With the future of the Uruguay international one step closer to a resolution, Rodgers is now ready to focus on further bolstering his squad before the September 2 transfer deadline.
Liverpool have been heavily linked with a move for Willian, who looks set to leave beleaguered Russian side Anzhi Makhachkala.
The Ulsterman dismissed claims that the Brazilian's Anfield arrival was imminent, but confirmed his intention to add numbers before the deadline.
He said: "We're confident of having one or two in before the window shuts. (Willian rumours) are just speculation really."
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