Local police reported at least 33 fans had been arrested after violent scenes, which saw the Barcaccia Fountain - located near the city's famous Spanish Steps - badly damaged.
A police statement claimed officers were pelted with bottles and other objects by visiting fans, resulting in a multitude of injuries.
Feyenoord were thrown out of the competition in 2007 after their fans rioted in the French town of Nancy.
"Rome has been devastated and wounded by this," the city's mayor Ignazio Marino posted on Twitter.
"We are in contact with the authorities and the Dutch Ambassador. It will not end here. I protested and demanded an explanation from those who are responsible for public order in this city.
"We found damage to the Barcaccia, which had just been restored. This violence is unacceptable and Romans will not be the ones who have to pay for it."
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