The 25 year-old handled the ball before scoring Liverpool's second goal against the non-league Stags at Field Mill.
When asked whether the Uruguayan, who has now scored 19 goals this season, should have owned up Rodgers told ESPN: "It's not Luis's job to do that.
"It's not been deliberate as it's pushed up and hit his hand. It's up to the officials to decide that."
The Carnlough man added: "There's no doubt it was handball, but the referee and the officials ruled it wasn't deliberate.
"I spoke to the fourth official when it was given because I couldn't see and he said it was [handball] so I can only assume they thought it wasn't deliberate.
"So obviously it was unfortunate for Mansfield and lucky for us that we got the goal."
Opening the scoring for The Reds was new signing Daniel Sturridge who struck seven minutes into his debut. Mansfield went close to scoring a few times themselves before Matt Green finally found the back of the net with 11 minutes of normal time remaining. The non-league side pressed for an equaliser but failed to capitalise on any of their chances.
"I'm proud of my boys, I thought they were a different level [during the] second half. I thought we stood off them and let them play in the first half," Mansfield boss Paul Cox told ESPN.
"We've done well against one of the best teams. We've a lot of positives to take out of it."
Cox also refused to criticise Suarez for the handball.
"I'd like to give the benefit of the doubt and say it was a reaction. He's a goalscorer and I think goalscorers put the ball in the net anyway," he added.
When asked whether he felt cheated, Cox said: "No I don't. For me to come out and say something like that I think would be quite cheap.
"If it had gone in the other end and one of our players had done it I think we'd have accepted it."
Liverpool will now play Oldham Athletic in the fourth-round of the FA Cup.