The Serbia international feels the English giants were by no means at their best and hailed Robert Lewandowski following his winning goal
Henrikh Mkhitaryan gifted BVB the lead early on with a shot from the edge of the area, only for Olivier Giroud to restore parity after some poor defending from Dortmund.
However, Robert Lewandowski eventually helped last year's Champions League finalists to the full three points with a composed finish after being set up by Kevin Grosskreutz.
"I don't think Arsenal were playing their best football - they were trying to play pretty safe," Subotic told the official Uefa website.
"They felt they were going to score one goal more than us through their patience and through their play, but we ran a lot and defended very well and had some great chances.
"We are obviously very happy with the three points. We came here not expecting anything but hoping for the best obviously. As the game progressed we always wanted more and more."
Subotic then went on to praise Lewandowski, arguing that it was only right that the Poland international decided the game in the visitors' favour.
"It was a huge relief," he admitted. "Robert had to fight for 85 minutes to get his goal and he definitely deserved it because it was a tough fight for him against [Per] Mertesacker and [Laurent] Koscielny. I'm happy for him."
Dortmund, Arsenal and Napoli sit joint first in Group F with six points from three games, with Olympique de Marseille yet to get off the mark.