Yossi Benayoun slotted home a consolation in the 3-1 defeat.
"We had the early chances, but Olympiacos played a very committed game and made a good battle," said Wenger.
"We lost too many balls in the first half and overall became a bit insecure.
"They were sharper than we were at 2-0, but we came back and then looked like we could equalise, but they scored the third goal. Overall Olympiacos deserved to win.
"Unfortunately for them it is not enough to qualify as Marseille made a super result in Dortmund."
Wenger added: "I am annoyed because we lost the game, it is difficult to single [anyone] out. Offensively and defensively we were not convincing.
"We could sense there was something more at stake for Olympiacos than us, and that made a difference."