Edinburgh were still in the game at 6-3 down at half-time but failed to live with the Blues in the second half ensuring they suffered a first Heineken Cup defeat of the season.
But Bradley, whose Gunners are currently ninth in the RaboDirect PRO12 table, believes his side are more than capable of getting back to winning ways next time out.
"I'm disappointed with our performance," said Bradley. "We shut down Dan Parks in the first half but didn't convert our territory into scores while Cardiff went in 6-3 up without doing very much.
"We made too many uncharacteristic errors and lacked the composure that I expect we'll have in more familiar surroundings.
"The difference between the sides wasn't that big and certainly isn't insurmountable going into next Friday's rematch at Murrayfield."
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