But after a disappointing start to the season Bradley's side have rectified a seven-game losing streak with back-to-back RaboDirect PRO12 victories over reigning champions Ospreys and Connacht.
They resume European hostilities this weekend with the first of a double-header against Racing Metro 92 on Saturday, the team they defeated twice during the pool stage last season on route to the Heineken Cup semi-finals.
And head coach Bradley is convinced his side can carry their improving league form across into the European break.
"We don't believe we are out of the tournament," Bradley told The Scotsman.
"We obviously have to get two wins in the next eight days when we play Racing home and away.
"Then nobody knows what is going to happen between Saracens and Munster.
"But, if we get two wins, we can look at the table after four matches and we'll know for sure whether we have something to play for in the last two games
"We've seen from our recent performances, particularly our win over Ospreys, that our pack has the ability to dominate the set piece and the contact area, and we will need a performance of that measure to establish a foothold in this game.
"Games like the two we played against Racing last season are not good for the nerves, but the fact we won both games is very good for us going over there this weekend. We don't fear them."