Police made at least 33 arrests in the Italian capital after trouble flared up ahead of the first leg of their last 32 tie, which ended 1-1 at the Stadio Olimpico.
Damage to the Barcaccia Fountain and violent scenes with police marred the build-up, but European football's governing body confirmed on Friday that the Eredivisie club will face no sanctions for the behaviour of their supporters.
Instead, it will be up to Italian police to identify any culprits and take necessary action against them for the trouble.
"UEFA condems the incidents of violence occurred in the city of Rome on Thursday," said UEFA in a statement.
"However, as the incidents occurred away from the stadium, it is outside UEFA's remit to act.
"It is a matter for the local authorities to investigate further."
Feyenoord were previously thrown out of the UEFA Cup in 2007 after their fans rioted in the French town of Nancy, but a similar sanction appears unlikely after this latest incident.
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