Aghayev entered Crystal Hall 3 to a rousing reception on Saturday morning, but was stunned in his -75kg kumite bout as Eltemur won 5-3 on his way to the semi-finals.
However, the Turkish competitor believes that the victory ranks among his best in the sport.
He told reporters: "I love [Aghayev] like my brother. I'm so proud to fight him.
"He is the idol and one of the best in the world. It's an achievement that I have never known before. It is the best of my life."
Aghayev still managed to qualify for the semi-finals with a win over Latvia's Ruslans Sadikovs to finish second in Pool A.