The match, which finished goalless, was suspended for two minutes shortly after the half-time interval by referee Gianluca Rocchi, allowing the stadium announcer to order offenders to desist before play was allowed to resume.
Rocchi was using a procedure introduced in the wake of Milan midfielder Kevin-Prince Boateng's decision to lead his team-mates off the pitch during a friendly game at Pro Patria in January, forcing the abandonment of the match and sparking new debate on the subject of racism in Italian football.
Although the Lega did not specify which three players it believed had been targeted by Roma fans, striker Mario Balotelli was seen raising his finger to his lips in a bid to silence visiting fans.
Roma captain Francesco Totti then approached the away end at San Siro during the suspension to reason with offending Giallorossi supporters.
A statement published on legaserie.it read: "A fine of 50,000 euros with a warning for Roma, whose supporters continuously addressed racially discriminatory chants to three players of the opposing team, prompting the referee to suspend the game for two minutes in order to make them desist from such reprehensible behaviour."
The warning attached to Roma's financial punishment could lead to the club playing future league matches behind closed doors should the events of Sunday night be repeated.
Roma's management responded quickly to the fine through the club's official website.
A statement read: "AS Roma condemns any form of racial abuse. This type of behavior from any football supporters, including ours, is completely unacceptable.
"We are committed to facing this issue head-on to rid our sport of this problem and to promote respect for all."
Earlier on Monday, the president of the Italian Football Federation (FIGC) pledged to push through legislation to help identify and exclude individuals found guilty of racist behaviour in Italian stadiums.
Giancarlo Abete joined FIFA president Sepp Blatter in condemning what the Swiss called "appalling" behaviour and, after claiming club fines are not working, he proposed more stringent sanctions for repeat offenders.
Abete told FIGC.com: "They (fines) are becoming a solution that does not solve the problem, because certain people don't care that their clubs are being fined 10,000 or 20,000 euros.
"In addition, this kind of fine does not act as a punitive sanction. We need to prevent certain people from gaining access to the stadium.
"If names are registered to tickets, these people will be prevented from accessing other parts of the stadium.
"This is a strong signal of our intent and after that would follow the entire closure of a stadium.
"This idea will be presented to UEFA's executive committee on May 24, where the main theme will be racism and I imagine that it will be endorsed as it falls in line with the committee's plans."
Inter Milan, Lazio and champions-elect Juventus have also been punished for the unsavoury behaviour of a minority of fans this season, encouraging Abete to work closely with the Lega, UEFA and FIFA to develop new initiatives to tackle a growing problem on the peninsula.
And Abete was impressed with the way Rocchi used the recently-adopted suspension procedure to handle the situation on Sunday night.
"There was great coordination between those responsible for maintaining public order, the referee Rocchi, his fourth official and the players," he said.
"The procedure introduced after Pro Patria-Milan worked, meaning that players can now consult with the referee to highlight certain situations.
"Each episode like the one yesterday [Sunday] weakens the image of football and it is a great sin that a hundred-odd irresponsible people can damage the image of the whole country, not just that of football."
Another moment of controversy in the game saw Milan midfielder Sulley Muntari dismissed shortly before half-time for physically restraining Rocchi as he attempted to book the Ghanaian for dissent.
Muntari on Monday received a two-game suspension and a 10,000 euro fine while Totti, who was later sent off for elbowing defender Philippe Mexes, will miss next week's season-ending meeting with Napoli.