Spurs manager Andre Villas-Boas has already said UEFA must investigate and the FA backed his stance on Friday.
"We were saddened and alarmed to see reports of violent incidents prior to the game as well as anti-semitic chants," an FA spokesperson said.
"The FA had a crowd control advisor present at the fixture who will provide an urgent report which we will pass on to UEFA as a matter of priority."
Thursday's match at Rome's Olympic stadium was overshadowed by violence after a Tottenham fan was seriously injured and nine others badly hurt when thugs wearing helmets and armed with knives and chains attacked a group of fans in a bar the night before the game.
Then during the match, home supporters sang "Juden Tottenham" during the first half, a reference to Spurs having a large Jewish fanbase and the supporters identifying themselves as the "Yid Army".
"It will take another investigation. It happened last time and it was acted upon quickly by UEFA," Villas-Boas said.
In October, Lazio were fined 40,000 euros by UEFA following racist chanting at White Hart Lane when the teams played the first game against each other in the competition and Lazio fans targeted Jermain Defoe, Aaron Lennon and Andros Townsend with monkey chants.
"We will have to wait and see if there is anything to act upon. If there is, UEFA have to act." Villas-Boas added.
Villas-Boas said the club was aware of the trouble and danger the club's fans had been in.
"It is an extremely difficult moment for them," he said.
"We have to be aware there is a police investigation and I'm not in control of all facts.
"But there is massive disappointment, and the fear they've gone through is hard. We give them a message of support. As a club, we will try to help them overcome this."
