The Germany international had to put up with derogatory chants from the stands during former club Roma's Copa Italia tie away to Lazio in March, while also allegedly being on the end of racial slurs from opposition players.
Following his switch from Rome to West London earlier this month, Rudiger is unwilling to draw a line under the sorry episode and will continue to challenge world football governing body FIFA to take a firm stance.
"I just want justice," he told reporters. "I want FIFA or the FA in Italy just to suspend those people who do that. It is not all the people in Italy who are like that. If we always talk about racism in Italy, people think that all Italians are racist people and it is not like that.
"I just mean those specific people who do it. Those people need to be banned from the stadium or fined. You feel alone. People love to say 'stay calm' or 'don't do anything'. It is easy for you to say those things when you are not black and you never feel what it is like.
"You cannot even put yourself in my position of how that feels. In that moment, it is like this. You are alone. You have to be strong. But each human is different. Someone takes it and doesn't react. Others react. I can understand both.
"I always wanted to play in the Premier League and it is now years since my name was first linked to Chelsea. Now I am here and I am very happy and want to thank all the people that made this come true. At the time (in 2016) it wasn't the right moment and now I am here. The whole squad has helped me feel welcome, they are very nice and very kind and very respectful. I like that."
Rudiger made his unofficial debut for Chelsea in Saturday's International Champions Cup defeat to Inter Milan, playing the final 37 minutes of the friendly match in Singapore.