"In a way it is only half-time in our battle with Newcastle and it is only half-time in the pool itself. The win was very good but all it has done is bring us back into line in the pool. There is a lot still to be done," he said.
Bradley is expecting quite a test from John Fletcher's Falcons when the sides meet at Kingston Park on Sunday afternoon.
"We have made this campaign hard on ourselves by slipping up in Brive at the outset. We still need to go to Newcastle and get something.
"They will be keen to make amends so it will be a bigger test for us. But you don't advance in this competition without crossing some big hurdles."
The Connacht boss has also been buoyed by the support which his squad has received so far this season from the Sportsground faithful, and they certainly made their presence felt during last Friday's memorable win.
"We have just had four home games on the trot, three of them were won and we were very disappointed with the loss to Ulster (in the Magners League). A solid support base is being built at the Sportsground and that can make a difference in a tight match. We saw that against Glasgow and we saw it again on Friday.
"I have said it before, the numbers, relative to other sides, may be small but my goodness they make an impact. Newcastle found that out on Friday night. What we need to do is build that support base and that will happen in time," he added.