The club considered the idea of giving fans the chance to gather at the stadium to watch the game together but decided against the option.
Communications manager Dave Allan explained: "We initially thought fans without a cup final ticket might like to gather at the Riverside to see the game.
Unfortunately all of our executive lounges are booked out for conferences, all senior staff will be in Eindhoven and the pitch is being taken up for its summer reseeding.
"On top of all that, the game is of course being screened on ITV1, so will be available in homes, pubs and clubs across the region so it was difficult to gauge the level of potential demand for a Riverside screening.
"We apologise for any disappointment this decision may cause our supporters but trust they will understand our reasons."