The club released a statement Tuesday saying a number of away supporters were prevented from entering the stadium while others were ejected from the ground.
"This behavior will not be tolerated at Chelsea Football Club," the club said.
"Those supporters will be banned from attending matches at Stamford Bridge in future, and in cooperation with Manchester United we have passed the details of those supporters to them so they can take appropriate action.
"Chelsea Football Club is a diverse and inclusive club and will always take firm action against all forms of discriminatory behaviour."
Manchester United, which won the tie 2-0, responded with a statement saying the club held a "long-standing commitment to equality, diversity and inclusion."
"We were the first club to sign up to the TeamPride coalition and continue to collaborate with Stonewall and other anti-discriminatory organizations in this area," the club said.
"Our fans were vocal as always in their support for the team last night and we appreciate that loyal backing.
"However, this song directed against Chelsea FC -- or any other club -- by some of our fans runs counter to our values.
"We will continue to engage in campaigns to raise awareness and fight discrimination in all forms."
The FA, English football's governing body, is not investigating the incident but says it took the accusations extremely seriously while remaining in regular discussions with official bodies on what language is deemed discriminatory.