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Swans fans called for the American to be sacked during Boxing Day's 4-1 home defeat by West Ham.
Bradley was only appointed in October but has lost seven of his 11 matches in charge, leaving Swansea second from bottom.
"I believe in my work and the message I give to the players," he said.
"Having said that, there is no getting around the fact when things go against us and when the margins are small, it makes it difficult.
"I have been in difficult situations before.
"I continue to look the players in the eye, challenge them and tell them the only way we can do this is if we all stick together and keep going."
Prior to the West Ham match, Bradley had admitted his future could depend on the outcome of the Boxing Day fixture and the home encounter with Bournemouth on New Year's Eve.
Defeat by the Hammers was Swansea's third in succession, and the heavy manner of the loss means Swansea have conceded 29 goals in Bradley's 11 games at the helm.
The Liberty Stadium crowd turned on the 58-year-old after West Ham's second goal, with chants of 'we want Bradley out' and 'you don't know what you're doing'.
The Swans are now four points adrift of safety in the Premier League, having conceded 19 goals in their last six games.
"At the moment, we are our own worst enemies. No matter what do, we seem to put ourselves in terrible spots," Bradley added.
"We all heard the response in the stadium today. It doesn't feel good but sometimes in football, you have to fight when everything is going against you.
"There is no magic formula, other than having a bunch of guys who don't give up and find a way to turn things in a better way.
"I said when I came here, I understood it was a difficult situation.
"I committed myself to the club, to work, fight, to do the job. I continue to be fully committed to that."
West Ham manager Slaven Bilic had some sympathy for Bradley, saying: "It would be crazy for them [Swansea] to change the manager again."
Former England captain Alan Shearer:
"Swansea just aren't working hard enough. There's no excuse for the second goal. Winston Reid gets above the two defenders - there's no way he should win the ball - but he gets above them because he wants it more, it means more to him.
"It was a big punt bringing Bob Bradley in, with his lack of experience of Premier League players and lack of experience in the Premier League. It was always going to be a big ask of him to keep Swansea up."
Swansea City manager Bob Bradley believes he can save them from relegation and remains "committed" to the Premier League strugglers.