Adebayor, who scored his side's away goal in a 4-1 defeat in the second leg that saw them scrape through to the quarter-finals, was allegedly subjected to monkey chants and plastic bananas were waved in one section of the half-empty stadium.
"It's very easy to hear the chanting so I'm sure UEFA will act on it," Tottenham manager Andre Villas-Boas said after Thursday's match, when the London side went through after a 4-4 aggregrate scoreline.
British newspapers lambasted Inter and the Italian game on Friday.
The latest racism incident follows last month's Milan derby in which former Inter striker Mario Balotelli was racially abused by fans, leading to Inter being fined 50,000 euros.
Lazio, who have a long-standing right wing element among their support, were ordered by UEFA last month to play two matches behind closed doors after racism by their fans in Europa League matches against Tottenham, Maribor and Borussia Moenchengladbach.
The Rome club have reached the last eight of the Europa League having beaten Stuttgart on Thursday, with the home leg played in an empty stadium. Their quarter-final home leg with Fenerbahce will also be without fans.
Juventus coach Antonio Conte has spoken out about the racist abuse afflicting Italian stadiums, saying that fans should get behind their own teams and not risk their side having to play matches behind closed doors.
"Songs against other teams don't get us going. Fans should concentrate on their own team, that's the best and gives us something extra," Conte said ahead of the Serie A leaders' match at Bologna on Saturday .
"I read about bans and I don't want songs like that to have us playing behind closed doors. We should do something so that from now until the end of the season it doesn't happen again."
Juve fans were accused of singing racist chants about AC Milan's Italy forward Balotelli last weekend.
Serie A decided the chants of "if you jump up and down Balotelli will die" were not of a discriminatory nature but were still offensive and fined the Turin club 4,000 euros.
Juve had to play a game behind closed doors in 2009 after Balotelli, then with Inter Milan, was racially abused from the stands with the chant "a black Italian does not exist".
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- Mario Balotelli