The 26-year-old was targeted by some Tottenham fans after he was involved in a clash with Son Heung-min that triggered a red card for the South Korean star.
Son kicked out at Rudiger after they collided and the German centre-back went to the turf clutching his stomach.
"It's just such a shame that racism still exists in 2019. When will this nonsense stop?," Rudiger tweeted.
"I really hope that the offenders will be found and punished soon, and in such a modern football ground like the Tottenham Hotspur Stadium with dozens of TV and security cameras, it must be possible to find and subsequently punish them.
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"If not, then there must have been witnesses in the stadium who saw and heard the incident."
In a four-part message on Twitter, Rudiger, who joined Chelsea from Roma in Italy in 2017, stressed that the issue should not be swept under the carpet.
However, he insisted the racism he experienced in his team's 2-0 win at their London rivals, resulted from the actions of a minority.
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"I don't want to involve Tottenham as an entire club into this situation as I know that just a couple of idiots were the offenders."
However, he added: "It is really sad to see racism again at a football match, but I think it's very important to talk about it in public.
"If not, it will be forgotten again in a couple of days (as always)."
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