The April 14 match at Udinese was suspended in the second half after Roma defender Evan Ndicka collapsed on the pitch and Serie A said the remainder would be played on Thursday.
Roma are also scheduled to play Bologna and Napoli this week before hosting Bayer Leverkusen on May 2 in the first leg of their Europa League semi-final.
"AS Roma with its results and four consecutive European semi-finals contributed to UEFA ranking and thus five slots for Italian teams in the next edition of the Champions League," the club said on Friday.
"Despite that, (Serie A) President (Lorenzo) Casini took today an unfair decision, as it holds, against AS Roma forcing us to face Bayer 04 Leverkusen at disadvantage," it added.
"This is a clear backwards step for the whole of Italian football."
