The Gunners left Dortmund on Tuesday with a point after captain Robin van Persie scored the opening goal on 42 minutes before Borussia replacement Ivan Perisic netted an equalisier in the 88nd minute of the Group F clash.
Van Persie scored after managing to shake off his marker Kehl for Arsenal's goal and the Dortmund captain admitted he was left kicking himself in the changing room at half-time.
"I sat during the half-time break and wanted to kick myself in the arse," the 31-year-old told German daily Bild after making only his third appearance of the season following recovery from injury.
"We played well, but because of a stupid mistake from me, we fell behind.
"Thankfully, it finished in a draw."
In their next Champions League game, Dortmund are at Marseille on September 28, the same night Arsenal host Olympiakos in their next Group F match.