Following the incident, there have been suggestions that Liverpool could offload the striker in the summer transfer window due to fears of the club's image being tainted by his latest controversial actions.
"Luis Suarez has anger management problems and issues, but you have to suffer the consequences," Barnes told the BBC Radio Five Live. "People talk about it reflecting badly on the club, but that is not true.
"It reflects badly on the player concerned. In terms of people saying that he will never play again for Liverpool I don't think that is true."
The Football Association could issue a lengthy ban on Suarez as they continue to investigate the incident.