"We are obviously very happy with the three points," Subotic told reporters. "We came here not expecting anything but hoping for the best obviously. As the game progressed we always wanted more and more.
"I don't think Arsenal were playing their best football, they were trying to play pretty safe. 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.
"[The winning goal] was a huge relief. [Lewandowski] 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] Koscielney and I'm happy for him."
Dortmund return to Bundesliga action on Saturday when they travel to Schalke 04.