Dortmund ran out 2-1 winners at the Emirates in a disappointing night for the Gunners, with goals from Henrikh Mkhitaryan and Robert Lewandowski.
A goal from Olivier Giroud appeared to give the home side a lift, but the German club won it late on with a swift counter-attack.
With Dortmund Champions League runners up last season - beating real 4-1 in the semi-final first leg on the way - and in red-hot form, a win for the away side certainly didn't seem out of the equation.
However, Subotic claims his side weren't expecting anything from the fixture and is obviously happy with the result.
"We are obviously very happy with the three points. We came here not expecting anything but hoping for the best obviously," he is quoted as saying on talkSPORT.
"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."
Dortmund, buoyed by their incredible away support, pressed the Gunners high up the pitch and made it difficult for Arsene Wenger's side to get into their rhythm.
The loss of Mathieu Flamini in front of the back-four was noticeable, though even with the Frenchman Arsenal would have struggled to play their usual flowing football.
Working from the front, Lewnadowski set the tone for his side's aggression whilst out of possession.
The Polish striker was rewarded for his effort late on as he finished a swift counter-attacks to send the visiting Germans into raptures.
And Subotic was particularly pleased for his team-mate:
"(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 Mertesacker and Koscielny and I'm happy for him.
"(The winning goal) was a huge relief," he continued.
The result leaves Dortmund top of the group on goal difference, and next up they welcome Wenger's men for a deciding clash.
Arsenal will be hoping to have Walcott back in time for the tie, with a lack of pace hindering Arsenal's attempt at breaking down the Dortmund back line last night.
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