The Reds had taken an early league against their non-league opponents through Daniel Sturridge, only for Suarez to use his arm to take the ball past the opposition goalkeeper before sliding the ball into the net to double his side's advantage.
However, Rodgers refused to condemn his star striker, who would draw further ire from the home fans by pointing to his hand in celebrating his strike.
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"I have just seen it again and there is no doubt it was handball," Rodgers told ESPN. "I think what the referee and the officials were looking was that it wasn't deliberate, which it clearly wasn't.
"I spoke to the fourth official after the goal was given and asked him if it was handball, because I couldn't see, and he said it was. So obviously it is unfortunate for Mansfield and lucky for us that we got the goal.
"It doesn't really happen in football, to be honest.
"You don't see it [happen] and it's not Luis' job to do that. He's gone in there, it hasn't been a deliberate handball - [the ball] pitched up and hit his hand.
"That's up to the officials to deem. That's why they get paid and that's why they are professional officials.
"Andre Marriner, I thought, was excellent today along with his officials. It's one of those things that was unfortunate."