The Azzurri defender was incensed by the act and pulled his shirt down to try to reveal the marks left by his opponent to the official during their 1-0 defeat.
FIFA have since opened disciplinary proceedings against the La Celeste hitman, and the Reds forward could be hit with a lengthy ban if the governing body find him to be guilty.
However, Butcher, who played in three World Cups for the Three Lions, believes that Suarez's latest actions have nothing to do with his club side, and thinks any suspensions imposed on the player should only count for Uruguay.
Speaking to Sky Sports News, the current Hibernian boss said: "I think it should just be an international ban. It was on the international scene, he was playing for his country, it's nothing to do with Liverpool, or whatever club he does go to if that is the case. But I think it should be an international ban.
"They could punish him for 24 games, I think that's the maximum they could issue that ban, so it'll be very interesting to see what they do.
"Domestically, he had the ban before with Liverpool but he could still play internationally as well so I think if it's in that arena it should stay in that arena.
"I saw the pictures last night and I just couldn't believe it. It's like deja vu. He's done it before and it looks like he's done it again!"
Suarez was banned for seven games while playing for Ajax in 2010 for biting Otman Bakkal, before having a 10-match suspension handed down to him for a similar offence on Bransilav Ivanovic in 2013.
The Uruguay international also sat out eight games in the 2011-2012 season, after he was found guilty of racially abusing Manchester United's Patrice Evra.