Crystal Palace are 16th in the standings, five points ahead of Swansea and one above safety.
Bradley has divided opinion among the Swansea faithful, with the American still searching for his first win since taking over from Francesco Guidolin last month, but encouraging performances have given the fans cause for optimism.
"Now they are just focussed on trying to make sure we put a bad stretch behind us, and on making it happen this week," Bradley told reporters.
"My number one message for the supporters is that there are things out there which are going to be out of our control and their control. But between the players, the staff and the supporters, we are in this together.
"We need to be together on Saturday at the Liberty... I want the players to feel the supporters are with them and I want the supporters to know the players will give everything for them. We need that togetherness."
(Reporting by Shravanth Vijayakumar in Bengaluru)
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