First half goals from Emad Mohammed and Hassan Ashjari were not enough for Sepahan as Al Sadd advanced to the semi-finals following a 4-2 aggregate triumph and despite a 2-1 defeat on the night in the Qatari capital of Doha.
After seeing their 1-0 first leg win overturned after the AFC Disciplinary Committee adjudged the Iranian side fielded an ineligible player, Sepahan had set about hauling back the 3-0 deficit after just seven minutes at Sheik Jassim Bin Hamad Stadium courtesy of Mohammed's strike.
Ashjari's spectacular dipping strike from the edge of the area after 27 minutes gave the visitors further hope, but Al Sadd regrouped and made sure of their passage to the last four through Mamadou Niang's superb individual goal with four minutes remaining.
"The first thing is to feel very happy. The first objective was the qualification and we did it," said Fossati, who guided Saudi Arabia's Al Shabab to the semi-finals last year.
"I think Sepahan started very well. We tried to pass and play a normal game. Unfortunately, the first shot from them was a goal. I think our team did not know how to control the emotional part of the game after that.
"After the first goal, we played well in the last 10 minutes of the first half. Sepahan showed in the first half how good they are. They took three shots and scored two goals."
Al Sadd are now scheduled to play Korea Republic's Suwon Samsung Bluwings over two legs in October's semi-finals.