Tavecchio was elected to the role of FIGC president on Monday despite remarks in the lead up to the ballot, when he referred to African footballers as "banana eaters" in a speech calling for work permits to be introduced into Italy's professional football divisions.
The 71-year-old has been widely admonished, but was still elected with 63.33 per cent of the vote, beating former Italy and Milan midfielder Demetrio Albertini in the contest to replace Giancarlo Abete - who left his post following the country's group-stage exit at the World Cup.
Italian Professional Footballers Association (AIC) president Tomassi believes that Italy will not be able to tackle the problem of racism unless Tavecchio is punished.
"It will be impossible to start any anti-racism campaign in Italy in the future if there are no sanctions for this president," Tomassi said in quotes reported by world players' union FIFPro.
"We all supported Albertini. He would be a choice for the future, he could change the current mentality. Tavecchio would not be just one, but ten steps back in time.
"Before the vote, everybody thought it would be impossible for him to be elected after the comments he had made.
"For the players, it is very difficult to feel represented by Carlo Tavecchio."
Tomassi also indicated that he would raise the question of a sanction for Tavecchio at the FIGC's next board meeting on Monday.
"We have to reflect on his remarks about foreign players," he added. "We need more than the simple rectification he has made. They are not a joke. We have to think what is the correct sanction.
"In Italy, we still have people in the stadiums who think that there are no black Italians. I think this year we should not be surprised when we see banners inside the stadium displaying 'Tavecchio one of us.'
"If we do not sanction Tavecchio's remarks, we cannot sanction supporters or players making racist remarks either. If you want to launch any campaign against racism in the future, you have to attack Tavecchio's remarks with force.
"We are protecting all the players and foreign players in Italy. And we also have a lot of Italian players outside Italy. What do you think about Italy's image? This is a disaster for everyone in Italy."
