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An "administrative error" was blamed when the Trust claimed former director Leigh Dineen had been reappointed to the board without its consultation.
The club's new American owners had previously apologised to the Trust for a lack of communication.
Bradley hopes fans get behind the side for Saturday's visit of Crystal Palace.
"Supporters speak up and voice their opinions," he said. "It's all fair. They are the heart and soul of the club.
"But supporters also know that when that team steps on the field, for that 95 minutes, the only thing that matters is what happens with the result."
The Swans are bottom of the Premier League and five points from safety, having failed to win since the opening day of the season.
Bradley has not won in five games since succeeding Francesco Guidolin as manager while Palace have lost their past five games - conceding 13 goals - and are 16th.
"We're just focusing on making sure we put a bad stretch behind us and it's going to happen this week," added Bradley.
"There will be plenty of time for the other things to work themselves out. But let's make sure that the relationship between the team and the supporters carries us through this stretch.
"I want the players to feel that support and the supporters to know the players are going to give everything for them."
Swansea signed Borja Baston, Fernando Llorente, Alfie Mawson, Leroy Fer and Mike van der Hoorn in the summer, but Bradley will look to the January transfer window in order to turn his side's fortunes around.
"The discussions have been positive about identifying ways we can improve the team. The idea is that we are going to look to improve our squad," Bradley said.
"We have a road ahead that will require looking at all the possibilities and fighting like crazy.
"You can make cases for different parts of the field [where we need to strengthen]. Just before January we will make a decision."
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Swansea City manager Bob Bradley says disagreements between the club's Supporters' Trust and board will not affect his team.