The Gunners have never lost every game in Europe since the dawn of the professional era and Bradley knows his side will be up against it in their final clash against Saracens who currently sit top of the Pool.
But after two late tries against Munster restored some pride, Edinburgh will go into the game desperate to build on that momentum and avoid their undesired place in history.
"We lost the game at home, our fifth loss, and that's not a good statement, but Munster came with the intention of winning the game and taking a bonus point, and we have to be conscious of that," Bradley told the Scotsman.
"Munster's best asset of the past two, actually 12 or 13 years, has been their ability to defend and turn defence to attack so, if we'd cut loose at the very start of the game, that could have been dangerous for us.
"They got three tries in seven-and-a-half minutes at Thomond Park [in the first Heineken Cup meeting], so our key issues were discipline and shape and growing into the game, they'd get frustrated and we could then pick them off.
"We did that and got two good tries, which was nice to see in this tournament."
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