A goal in injury time saw Dempo go down to Al Safa 0-1 in their first leg of their AFC Cup semi-final at the Sports City Stadium in Beirut on Tuesday.
Hamze Aboud scored the only goal of the match following a corner.
Following a clearance by the Indian champion club's defence, Aboud controlled the ball with his chest and essayed a powerful shot that went off the crossbar and crashed into the net.
The victory gave the Lebanese side a slender advantage before the second leg of the semi-final at Hyderabad's Gachibowli stadium on October 21.