The Uruguayan striker caused controversy yesterday afternoon when he bit Chelsea defender Branislav Ivanovic on the arm during a match at Anfield - an act that he has since been charged for by the Football Association.
Some pundits have called for the Reds to sell their leading goalscoring at the end of the season in response to his actions, but Neville has described that demand as "nonsense".
"He's made a huge mistake and he is going to have to pay for it," Neville said on Sky Sports News. "I don't go along with [Liverpool have to sell him] at all.
"You hear all this media frenzy - 'throw him out of the country' and things like that. The idea that Suarez should be thrown out of the country or should never play for Liverpool again is nonsense and it is an overreaction.
"He's made a big mistake and he knows it. He's now got to win people back and start again. When you make mistakes in life, you've just got to get better."
Suarez is likely to learn what punishment he will receive from the English governing body on Wednesday.