Dzeko, 39, and Tadic, 36, were nowhere to be seen as Fenerbahce came from behind to beat Konyaspor 2-1 in their last game of 2024-25.
The veteran duo were set to receive commemorative plaques after the game but ultimately decided to stay away due to the risk of fan unrest following a disappointing campaign.
Tadic later released a statement saying: "It was a decision we made together with Dzeko not to play in the last match.
“We didn't want to damage Fenerbahce's image. The fans have always supported us. I would have preferred it to be in the stadium, but the ambiance is not very good at the moment. That's why it's better to be that way."
Both players look set to leave the Turkish giants this summer with their contracts due to expire now the season is over.