In a game dominated by Dortmund, it was the French side who were more clinical as a brace from Andre Ayew and a Loïc Remy goal were enough to send them top of Group F.
Speaking after the match, Klopp bemoaned his side' defensive frailties which cost them dearly.
"Tomorrow [Thursday] morning nobody will care how this result ended up like it did. We put a lot into the game, but made a few mistakes," he was quoted as saying in UEFA.com.
"We had long spells of dominance during the match, especially at the beginning of the second half. All of the goals we conceded were a surprise, but we've got only ourselves to blame.
"After we conceded the first goal we lost some of our organisation. We allowed them to counterattack more. Even though Marseille scored three goals, we had better chances than them.
Götze was one of the star performers of the game, leading the show inside the Stade Velodrome. But it all accounted to nothing.
"Mario Götze could easily have scored a few goals today and Mats Hummels made one mistake which we were punished for. Once they scored a third goal, it was all over for us."
The defeat leaves Dortmund third in Group F with just a point from the opening two games.