A report on the website of the Sporting News contained un-named players questioning the work of Klinsmann and raising the issue as to whether the team was behind the German coach.
"I saw it. I think it is shameful. I think it is embarrassing," said Bradley, the son of Klinsmann's predecessor Bob Bradley.
"On every team in the world, not every guy is going to be happy, on every team in the world there are going to be guys who go back to their room and talk with their room-mate about things that they wish were different, things they wish would be done another way, but that is normal.
"But you cross a line when you take those thoughts and you take your disappointments outside of the team and outside of the inner circle. So for me, it doesn't help anybody, it doesn't help anything that we are trying to do this week," he added.
The report said players had questioned Klinsmann's training regime and tactical approach for the 2-1 loss to Honduras in San Pedro Sula in the United States' opening game of the six-team final qualifying round in the CONCACAF region in February.
A seething Bradley made no secret of his feelings towards the players who had made their feelings known to the media instead of keeping it inside the locker-room.
"When you play on a team you have a chance everyday to give everything you have and part of that means having the balls to say things to guys to their face, having the balls to say things in front of the team.
"In those ways it is really disappointing that in a week as important as this, with so much on the line, that you would have something like that happen.
"The challenge of every guy in our team right now is to step on the field on Friday night and make sure to every American watching that there is no sign of anything that has gone wrong this week," he said.
After Friday's game at Dicks Sporting Goods Park in Denver, the United States face archrivals Mexico in Mexico City on Tuesday.
"It is our job to represent ourselves and represent our country in a way that makes everybody proud. I think that we have let ourselves down a little bit in that way but the best part about sports is that when you step on the field you can put everything right."