The Turkish team prevailed over their opponents in Istanbul but were unable to repeat the achievement in Tuesday's return match, but they could still grab a last-16 place
The Turkish side won the pair's matchday three encounter in Istanbul by the same scoreline, but were unable to replicate that feat in Lisbon.
It leaves them three points adrift of second-placed Atletico Madrid, who they face in their next fixture.
Another loss would eliminate them from the competition, but the coach is still aiming to finish in the top two rather than consolidate third place and a subsequent Europa League berth.
"It's too early to talk about the Europa League, we have two more games to go," Hamzaoglu said.
"Maybe it seems difficult, but I hope we will chase it. We will play to win the next two games."
Hamzaoglu was pleased with how his team approached the game, but felt Benfica's second goal was the decisive factor.
"We played as you should against Benfica here," he added.
"We pressed until the end but unfortunately we couldn't find the equaliser.
"At 1-1, we were about to take some attacking steps, but the unexpected second goal kept us at the back."