Crook Town parted company with manager Richie Hill after beating first division Ashington 2-1 in the Vase on Saturday.
Hill, who took charge last season, missed Saturday's game, and along with assistant Gary Hornsby was relieved from his post as manager yesterday morning.
Chairman Steve Buddle said: "We had a poor pre-season, and results haven't gone our way - we're in the bottom four of the table.
"The supporters are also turning their backs on us, so we thought it best to bring somebody new in.
"We have got nobody in mind, we'll listen to applications."
All the goals came in extra time Darren Kokes, signed before the game from West Auckland, put them in front from 25 yards.
Kristian Dinsley added the second from the same distance before the end of the first period. Lee Anderson pulled one back in a scramble.
Bishop Auckland manager Peter Mulcaster admitted his side was lucky to go through to the next round of the FA Vase after a 1-0 victory at Esh Winning in the first qualifying round of the competition.
"Esh must be gutted to lose, but for a change we carried some luck," said Mulcaster.
"We had two chances cleared off their line, but they hit the post three times at the other end. In general play they were better than us."
There were only 20 seconds remaining in normal time when Bishops scored the goal that mattered, Dane Wilson heading in a Dale Mendum cross.
Bishops are now at home to Winterton Rangers, who easily beat Ryton 3-0.
South Shields earned a draw at Thackley, drawing 1-1, Lee O'Donovan scoring.
Morpeth saw off North Shields 5-0, with Kevin Henderson setting them on their way after just 80 seconds.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article