After making 13 changes from the side that lost 17-12 to Glasgow on New Year's Day, Bradley admitted he was expecting a response from his troops, but tries from Nick De Luca and Alun Walker were in vain as the Ulstermen ran out comfortable winners.
He said: "It's was not what we were expecting and not what we were looking for.
"We were careless with ball in contact and you cannot do that against quality opposition. We made them look very good. I thought they were very good on the night but we just made it far too easy for them.
"I suppose first of all you have to give credit to Ulster. They played very, very well but we made it far too easy for them."
Next up for Bradley's side is a trip to Racing Metro in the Heineken Cup on Friday and, as Pool 2 leaders, the Irish coach is expecting a safe passage through to the knock-out stages for the first time since 2004.
He added: "We have work to do in terms of getting our heads for next week. We have to pick ourselves up off the ground on the basis that it wasn't a good day for us.
"We've two crucial matches coming up and Ulster are in the same position with two critical Heineken Cup matches in the next two weeks."
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