Inter reacted with dismay and "great sorrow" on Friday as the Italian FA refused to overturn the red card shown to Romelu Lukaku when he stood up to racist abuse against Juventus.
The Belgian striker converted a penalty in the fifth minute of stoppage time to earn Inter a 1-1 draw in the Coppa Italia semi-final first leg on April 4 at the Allianz Stadium.
He then used his finger to shush the home fans' vitriol and that reaction was deemed a bookable offence by referee Davide Massa.
Lukaku had already been booked for a foul in the 80th minute, so the second yellow card saw him dismissed.
The Inter frontman called for action from Serie A officials after being targeted for abuse, while team-mate Edin Dzeko described the treatment from the Juventus fans as something "that should never happen".
FIFA president Gianni Infantino labelled the abuse "unacceptable" and called for those responsible to be punished.
A partial stadium closure was initially imposed on Juventus as a result of Lukaku being targeted, with the section from where the abuse came ordered to be shut for one game, but that decision was overturned this week.
An appeal against Lukaku's punishment was submitted by Inter to the Italian FA – the FIGC – but that was rejected on Friday, meaning the on-loan Chelsea player must miss next Wednesday's second leg.
In a statement, Inter said: "The FIGC's National Court of Appeal today confirmed the suspension of Romelu Lukaku, who will be unable to participate in Wednesday's Coppa Italia semi-final.
"FC Internazionale Milano feels it must consolidate its support for the player and expresses great sorrow at the fact that the victim has become the only guilty party."