The match in Novigrad, Croatia, was stopped moments before half-time when City coach Patrick Vieira led his team off the pitch having complained to the referee.
A statement issued by City said that an "alleged incident of racial abuse" towards midfielder Seko Fofana had been behind Vieira's actions.
However, Croatian club Rijeka have rejected that any such incident took place.
"We strongly reject unfounded racism allegations mentioned in the statement Manchester City has posted on its website and want to stress that Rijeka itself had six players from Nigeria on the team," Rijeka said in a statement issued on Wednesday.
"We also want to point out that HNK Rijeka, in cooperation with FARE (Football Against Racism in Europe), has been supporting the campaign against racism for years and we strongly condemn every such incident."
Rijeka coach Ranko Buteka also suggested City had walked off the pitch for no other reason than they were 1-0 down and had just been reduced to 10 men following the dismissal of Fofana.
"After our first goal, we expected more pressure from City but we remained the dominant team in all departments and had several opportunities to score again," Buteka told Croatia's national news agency Hina.
"They responded with more aggression, which resulted in a red card for them.
"While the first tougher tackle on Dangubic could be classified as reckless, the really violent tackle on Marko Marcius only a minute later was unjustifiable, so the Manchester midfielder was rightly sent off.
"What ensued was something rarely seen, even in friendly games.
"Perhaps he had expected an easier rival, against whom they could easily dominate and easily score, but this wasn't the case against us."
