Dortmund dominated the first hour of the UEFA Champions League Group F clash in Germany on Wednesday, but failed to capitalise on their superiority.
Henrikh Mkhitaryan and Jakub Blaszczykowski went close to giving Jurgen Klopp's side the lead, while Marco Reus scored but saw his effort ruled out for offside.
It was Arsenal who claimed the only goal, however, as Aaron Ramsey continued his fine form by beating Weidenfeller with a header - the visitors' first attempt of the match.
Arsenal finished strongly but Dortmund had 13 shots on goal to the four of their opponents and Weidenfeller was insistent his side should have claimed at least a point.
"Football can be cruel at times," he said afterwards.
"We were stunned after conceding the opener, but overall we had more chances and should have got something from the game."
Dortmund, who lost last season's Champions League final to Bayern Munich, are now three points behind both Arsenal and Napoli with two matches remaining.
Next up for Klopp's men is a crucial home fixture against Napoli on November 26.
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