The Uruguay international returned to training with the first-team squad on Friday having been exiled for more than a week by Rodgers, who said the striker's attitude and performances had not been up to scratch.
Suarez claimed Liverpool had reneged on a deal agreed last summer to allow him to leave if a Champions League club came in for him, with Arsenal having had two bids for him rejected.
However, he was at Anfield on Saturday to watch the 1-0 Premier League victory over Stoke and he received a ripple of applause from the small amount of home fans assembled inside the ground as he walked around the edge of the pitch with his daughter an hour before kick-off.
"I am satisfied with how everything has been resolved and we as a club are looking to the future," said Rodgers, who refused to confirm whether the player had apologised as he said he would have to in order to be reintegrated.
"There is nothing to be said there. I won't be saying anything on Luis Suarez and that is only purely out of respect for the (other) players."
Suarez is suspended for the first six matches of the campaign after biting Chelsea defender Branislav Ivanovic last season.
On Suarez's appearance and reception at Anfield, Rodgers added: "He is a part of our team and club and the supporters are a class act here.
"He's back in the group, he's smiling and happy, and we'll move on."