The U.S. fell behind in the first five minutes but rallied to take the lead at 2-1 before Portugal hit back to tie the match on the final play of the game.
The U.S. would have advanced to the knockout stage with a win, and a draw means they must still try to earn points against Germany to ensure they move on. But the draw against the team ranked fourth in the world by FIFA still gives the U.S. a strong hope to move out of the so-called group of death.
"The effort was incredible. It's disappointing not to close it out," Bradley said. "We talk all the time about working hard and how we respond in difficult moments. Tonight was another example of us showing everybody who we are and what makes us a good team. Soccer can be a cruel game sometimes.
"Crazy game. We put so much into it. After a difficult start, the response, and the commitment, the effort was incredible. Difficult conditions and still we found a way to push through, and really, every guy left everything on the field."
Bradley was involved in the final play as the U.S. tried to close out the final minute of stoppage time. He received the ball just inside Portugal's half but quickly lost possession. Portugal passed down the wing to Cristiano Ronaldo, who delivered a perfect cross for Silvestre Varela to head home.
After the match, Bradley recalled the final play in an interview with ESPN.
"Obviously, the end of the game, we're trying to move ourselves out and make the game as difficult for them [as possible]," he said.
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"The ball popped up, and I was able to make a few quick steps and get there. It was tight, and unfortunately I wasn't able to make a good enough play to keep it for us or get a foul. At that point, the ball turns over and it's up to us to deal with the situation."
Bradley at times stopped himself as he tried to find the right words to explain how he can move on from the mistake.
"Certainly, the way it ends, you rack your mind thinking, 'Can you do this better, can you do that better?'" Bradley said. "But the reality is still that, over the course of a game, there's a million of these kind of plays and you can't let these plays -- they go on in the course of a game and there's nothing else to it."
Asked if he blamed himself for the U.S. dropping points, Bradley said, "I put my heart and soul into every game, every time I step on the field. ... I'm proud of that and proud every time I play, and there are certainly no regrets in my book."
As for the Americans' comeback after conceding early, Bradley revealed that resilience is a large part of the team's mentality.
"That's who we are," he said. "We talk all the time about what we're like on the hardest days. When the spotlight comes on brightest and the biggest tests come, what are we like? How do we respond in difficult moments? And I thought tonight was another example of us showing everybody who we are and what makes us a good team."
Bradley: It's a cruel game sometimes
ESPN's Jeremy Schaap asks U.S. midfielder Michael Bradley whether he was at fault for Portugal's game-tying goal.