Turkey picked Hungary apart in a 6-1 aggregate scoreline thanks to goals from Hakan Calhanoglu, Guler and Abdulkerim Bardakci.
During the second leg, Guler shushed Szoboszlai as the pair argued over a decision. The Hungarian laughed at the 20-year-old who showed a lack of respect.
Nemzeti Sport Online posted a photo of the incident on Instagram, prompting Szoboszlai to reply "1088", which refers to the number of minutes Guler has played for Madrid this season in what is a brutal blow for the teenager.
Guler has made just 31 appearances under Madrid manager Carlo Ancelotti this season with 21 of those have been off the bench which is shocking looking at Madrid's injury issues this season.
In comparison, Szoboszlai has played 2887 minutes for Liverpool and scored seven goals while managing six assists under manager Arne Slot as he edges closer to the Premier League title.
Inter Milan's Calhanoglu spoke on Guler's situation and suggested that he deserves more minutes at the Spanish side.
"I don't know what his situation is at Real Madrid, that's why I don't want to get too involved in this situation because, in the end, he knows more, although of course I want and believe he deserves to play more minutes.
"Arda is a very important player, he's like a little brother whom I love very much. I would like him to come and play with us, although I don't know if that's true."