But Bradley said that Connacht were now in control of their own destiny and he praised the squad for the way they have set up Friday night's crucial Pool 3 clash with Brive.
Last Sunday's 60-0 win away to Spanish side Cetransa El Salvador, along with favourable results elsewhere, has set up Friday's winner-takes-all match at the Sportsground (6.30pm).
"There is still a big battle to face but at least we can now control our destiny," Bradley admitted.
"Brive are not getting the reward their performances deserve this season but we know they are formidable and probably should have won in Newcastle.
"But we have done well at the Sportsground this season and having a big vocal crowd behind us will give us an edge.
"It should be a great occasion. It is an exciting climax to our campaign at the pool stages and it would be another special night in the Sportsground if we could get the home victory," he said.
Bradley said that he was pleased with the way Connacht dealt with the challenge of Cetransa El Salvador at the weekend.
"In matches like that where you're expected to win, it is important to keep your shape. We emphasised that before the match and at half-time and it enabled us to control the game from start to finish."