The Parisiens were taken by surprise during a lively first half that saw Vladimir Weiss cancel out Edinson Cavani's opener, but took control in the second half thanks to a headed double from Thiago Motta and a first goal for 19-year-old summer signing Marquinhos.
Blanc admitted that his side were too slow in finding their feet at the Karaiskakis Stadium, but was thankful that Olympiakos' aggression looked to have cost them on Tuesday.
The ex-France boss, 47, told beIN Sport: "The first half we were a little sluggish, because we had problems with positioning on the left side.
"Olympiakos also had a lot of energy to press us and caused us problems by creating opportunities and corners. Nevertheless, we opened the scoring, but we did not hold it long enough to settle in the game.
"The second half was much better, positioning was better. I also sincerely believe that the pace of Olympiakos fell by the wayside because, in the first half, they were very aggressive."
PSG now sit top of Group C on goal difference and face Benfica, who also won their game over Belgian side Anderlecht, in the next round of fixtures.