The English centre-half joined the Serie A side on transfer deadline day, crossing over on loan for a season from the Red Devils after it became apparent he was no longer a first-choice selection at Old Trafford.
Smalling was still at the Theatre of Dreams when Paul Pogba and Marcus Rashford were racially abused, and after making the move to Italy - the scene of racism directed at former team-mate Romelu Lukaku - he called for change with a problem he believes is a worldwide issue.
"I think racism is unacceptable and should not be stood for. It is not an issue just in Italy, it is around the world," Smalling said.
"There needs to be a change, there will be generational changes and younger people will have a different perspective.
"But it does happen, not just in Italy but around the world, and it is very sad and unacceptable that it still happens in these modern times."
Smalling is yet to make his debut for the Giallorossi after being an unused substitute in the 1-1 draw against city rivals Lazio on Sunday.
The 29-year-old will be hoping to make his first appearance for Roma after the international break in September 15's home match against Sassuolo.
Having made more than 300 appearances for Manchester United in all competitions, Smalling is confident his Premier League experience will lead him to being a success in Serie A.
"There is a lot of responsibility on the defence as a whole [in Italy] and the centre-backs too, but that is something I enjoy. I like to push up high, play high up the pitch, and the manager wants us to be high," he said.
"I am a defender that likes to defend on the front foot so I think this is the perfect type of football for me and hopefully it allows me to show my real qualities.
“I think Serie A has always been a goal of mine to play in one day, because as a defender if you get the chance to experience Serie A you want to do it.
"I think I’ve played a lot in the Premier League and now I can bring my qualities that I’ve learned to Italy, and that is something I am looking forward to."