The Uruguay international returned to training with the first-team on Friday having been exiled for more than a week after criticising the Reds boss, who said his attitude and performances had not been up to standard.
Suarez claimed the club 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.
"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 still suspended for a further six matches for biting Chelsea's Branislav Ivanovic in April, but he was at Anfield to see his side win 1-0 against Stoke.
His pre-match walk around the pitch's perimeter brought muted applause and not the rapturous welcome he had received when he played in Steven Gerrard's testimonial a fortnight ago at Anfield.
"He is a part of our team and club and the supporters are a class act here," said Rodgers.
Rodgers had earlier described Suarez as "back...smiling and happy" in his pre-match interview with BT Sport.
Suarez went public with his grievances last week after a second bid of £40,000,001 by Arsenal, which they thought should have triggered his departure, was rejected by the Merseysiders.
Liverpool have always maintained there was no release clause as such, only a requirement to notify the player and begin negotiations should they wish.
Suarez seemed much happier before Saturday's game however, carrying daughter Delfina around the edge of the pitch to a ripple of applause from the smattering of fans assembled inside the ground an hour before kick-off.
He even stopped to shake hands with former referee Mark Halsey at pitchside before disappearing down the tunnel, emerging less than 10 minutes later to make the walk back to the executive boxes in the Centenary Stand on the opposite side of the ground.
A small group of Stoke fans booed as he walked past them but there was more applause and the odd cheer.