Uruguay and Liverpool striker Suarez has been given a four-month suspension from all football-related activity by FIFA for the incident in the World Cup Group D game between the two sides on Tuesday and has been suspended for nine international matches.
Suarez has left Brazil and flown home to Uruguay but Chiellini is not convinced world football's governing body have taken the correct course of action and hopes the striker will be allowed to return to be with his team-mates for their last-16 match with Colombia on Saturday night.
"Now inside me there's no feelings of joy, revenge or anger against Suarez for an incident that happened on the pitch and that's done," said the Juventus centre-back.
"There only remain the anger and the disappointment about the match. At the moment my only thought is for Luis and his family, because they will face a very difficult period.
"I have always considered unequivocal the disciplinary interventions by the competent bodies, but at the same time I believe that the proposed formula is excessive.
"I sincerely hope that he will be allowed, at least, to stay close to his team mates during the games because such a ban is really alienating for a player."
Argentina legend Diego Maradona, meanwhile, said FIFA's punishment of Suarez is 'shameful' and believes it is a politically-motivated decision.
Maradona declared his unconditional support for the controversial Uruguay international, who will be unable to play any football until October 26, on his television show 'De Zurda' on Thursday, wearing a T-shirt bearing the message "Luis, we are with you".
"The FIFA sanction is shameful, they have no sensitivity towards the fans, they might as well handcuff him and throw him in Guantanamo," said Maradona, who himself was given a 15-month ban from football during the 1994 World Cup for testing positive for the banned stimulant ephedrine.
"The sanction on Luis is a way of punishing Uruguayan clubs for asking CONMEBOL (the South American confederation) for a fairer share of money. It hurts that they have cut short the career of a lad who is a winner. It's an excessive suspension, FIFA cannot talk about morals to anyone.
"Suarez didn't kill anyone. This is an unjust punishment."
Betting website 888poker has confirmed it has dropped Suarez as its ambassador following his bite on Chiellini.
A statement from the company read: "888poker signed Luis Suarez following a fantastic season for which his achievements were widely recognised.
"Regrettably, following his actions during Uruguay's World Cup match against Italy on Tuesday, 888poker has decided to terminate its relationship with Luis Suarez with immediate effect."
Suarez's boot deal with adidas could also be in jeopardy after the sportswear manufacturer announced on Thursday that it too would consider its partnership with the 27-year-old.
Suarez was last year banned for 10 games in domestic competition after biting Chelsea defender Branislav Ivanovic while playing for Liverpool, and in 2010 when with Ajax, he served a seven-game ban after biting PSV Eindhoven's Otman Bakkal.
A statement on Thursday read: "adidas fully supports FIFA's decision. adidas certainly does not condone Luis Suarez's recent behaviour and we will again be reminding him of the high standards we expect from our players.
"We have no plan to use Suarez for any additional marketing activities during the 2014 FIFA World Cup. We will discuss all aspects of our future partnership directly with Suarez and his team following the World Cup."
In addition to his latest lengthy ban, Suarez was also fined 100,000 Swiss francs (just under £66,000).