The Welshman was caught in possession just outside his own area in the build-up to Henrikh Mkhitaryan's opener for the Bundesliga giants on Tuesday night.
And despite thinking that the Gunners deserved at least a draw, Ramsey conceded he was disappointed in himself for gifting Dortmund a goal.
"A draw would have been a fair result after the way we played in the second half," he told Arsenal's official website.
"I felt like we were in control of the game but then we switched off for 30 seconds, we were in their box and 30 seconds later the ball is in the back of our net.
"I was disappointed as well with the way they scored their first goal, I got caught on the ball and that was disappointing.
"We were a bit slow to start but I thought after about 25 minutes we got into the game, we got our goal and then we took that into the second half."
Ramsey also praised Arsenal's character to come back into the game and insists they will learn from not taking their chances in the second half.
"We were in control of the game, we didn't look like we were going to concede, but then we did. That's what happens [when you switch off].
"We showed good character getting back into game… and we created a few chances in the second half and hit the bar. On another night we may have taken the lead but we have to learn from the way we defended for the second goal."
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