Spurs striker Emmanuel Adebayor was reportedly the subject of much of the abuse, with some fans apparently making monkey chants and another waving an inflatable banana.
The Togo striker scored in extra-time of the last-16, second leg match to help Spurs advance on away goals after the tie finished 4-4 on aggregate.
UEFA has confirmed it is investigating "racist behaviour of supporters, insufficient organisation and the throwing of missiles and/or fireworks."
The abuse was reported to UEFA by the match delegate and anti-discrimination body FARE and the case will be dealt with on April 19.
Spurs boss Andre Villas-Boas said after the game: "It was very, very easy to hear the chanting so I am sure that UEFA will act on it.
"It's difficult for Inter Milan because it is something that in some way has happened before. It doesn't mar the game but it is something that should have been avoided."
Tottenham's director of football administration Darren Eales had also urged UEFA to act, telling Sky Sports News: "It is terrible and has no place in football.
"It is a problem that football has had over time...in England from a fans retrospective we are perhaps in a better place than some of the other countries.
"I think it is important for UEFA to set a precedent and they lead European governance and it is important for them to make a stand."