Supporters of the Pittodrie club who attended the third qualifying round first leg complained the area of the stadium set aside for them was like a cage with poor toilet facilities.
Others said they were given fines for drunkenness in the 2-0 defeat.
The club have confirmed they informed the match delegate of the situation.
However, Rijeka say one of three buses the Croatian side provided for visiting fans was “significantly” damaged.
A statement said: “According to the decision of the police, because of their safety the Aberdeen fans were detained for 30 minutes after the match.
“HNK Rijeka also hired (although it did not have the obligation) three buses to transport Aberdeen fans from the city centre to the stadium and vice versa in return, of which one bus was significantly damaged by the fans because the lighting on the bus roof was completely damaged. The material damage that HNK Rijeka has to pay has been recorded.”
Supporter David Mitchell, 38, who was at the game, told BBC Scotland: “There was a light broken when people banged on the roof, however they were just pulling random people for it – some who were not even on that bus – and fining them.”
The second leg will be played at Pittodrie on Thursday night.