Carver’s side slipped deeper into the relegation mire after an eighth successive defeat to Leicester City at the weekend.
The performance at the King Power Stadium, where Newcastle were beaten 3-0, was one of the worst of the Premier League era.
And the loss left the club is just two points above third-from-bottom Sunderland, who have a game in hand.
Many fans want head coach Carver to be relieved of his duties before Saturday’s home game against West Bromwich Albion given his dire record as head coach.
But the odds are stacked against Steve McClaren, the frontrunner to take the job in the summer, taking charge for the final three games of the season, despite Derby County’s campaign having ended at the weekend.
For his part, Carver – who accused United defender Mike Williamson of getting sent off “on purpose” in Saturday’s 3-0 loss at the King Power Stadium – has no intention of stepping down.
“I’m not going anywhere until someone comes to me and tells me otherwise,” said Carver.
“I’m not a shirker, and I’m not going to hide from anyone. I’m going to stand there and take it, because I have to.”
Carver had a brief conversation with managing director Lee Charnley after the Leicester game.
He said: “I had a quick chat with Lee Charnley, but it was nothing serious.
“He was basically just asking how I was and how I was feeling. It was a nice, calm conversation.”
Newcastle have won just two of 16 league games under Carver, who took over from Crystal Palace-bound Alan Pardew at the turn of the year.
And, astonishingly, the 50-year-old has admitted that there is a chance some of his players simply are no longer listening to what he is saying on the training field and in the dressing room.
“If I’m honest, I have to admit there’s a chance they’re just not listening to me,” said Carver.
“That might be one factor of many, and you have to consider it. You have to consider it and take it into account.
“But it might be a lot of other things – we might not be good enough, we might not have enough desire to want to defend in the box or score at the other end.
“There’s lot of factors, but I won’t deny that (the players not listening) could be one of them.”
Meanwhile, Carver refused to talk about McClaren’s situation, only offering him “commiserations” over Derby’s failure to secure a play-off place.