The Magpies boss is under pressure as his team have gone eight matches without a win and fell to a 1-0 defeat at Sheffield United - who hadn't claimed three points in the league until Tuesday's (12.01.21) match - but Bruce insists that he has no plans to quit.
He said: "I'll never ever walk away from a challenge.
"I've been in it long enough to have that respect, but I understand especially watching the first half - we weren't good enough and I take the responsibility for that, because I picked the team."
Bruce believes his team have made a "decent start" to the season and suggested that difficult opponents in recent matches had contributed to Newcastle's winless run.
He told reporters: "I think we've had, apart from the last month which we knew would be difficult with the run of fixtures we've had, we've given ourselves a decent start to the season."
Newcastle were beaten by Billy Sharp's second-half penalty given as a result of Federico Fernandez's handball but Bruce slammed the video assistant referee (VAR) for its role in the decisive call.
He said: "I have to say the decision for the penalty is poor.
"I'm asking the referee now why when he doesn't give it to start with he says Fedi's intentionally handled it, I don't see how he can say that - when you're running, your arms are going to move, and it looked a foul to me. Billy Sharp's got a hold of his shirt.
"I thought the referee got it spot on when he didn't give it, if that's intentional handball and VAR's supposed to be clear and obvious."