Hughton was targeted on the social media site in the wake of City's 1-0 win at Stoke last weekend.
Speaking ahead of Norwich's Sky Live clash with Chelsea at Carrow Road on Sunday, he admitted more needed to be done to combat the problem of racism.
"I'm saddened and disappointed by alleged racist comments on social media. It's been passed to the appropriate people to be dealt with," said Hughton.
"As a club we are working hard to tackle discrimination, as are organisations like Kick It Out. That work needs to continue."
As for the game with Chelsea, Hughton says they will take confidence from their display against Stoke but conceded they will face a much stiffer test against Jose Mourinho's side.
"We played really well at Stoke and there's been a good, confident feel throughout the group during the week," he added.
"Alex Tettey did very well at Stoke which allowed (Leroy) Fer and (Jonny) Howson a bit more freedom. Alex is an excellent, competitive player
"Chelsea have quality throughout their squad. We have to make sure our work ethic is spot on again and that we keep possession well."
Norwich take on Chelsea, live on Sky Sports 1 HD from 12:30pm on Sunday