They are now in real danger of failing to finish in the SPL top six on top of crashing out of the Active Nation Scottish Cup to Raith Rovers last month.
It means McGhee has won just eight of his 34 competitive games in charge.
"What is the crisis? That we've not made the top six - yet? That we've not won for 10 games?" said the Dons boss, who earlier this week insisted it would be "grossly unfair" were he to be sacked as manager.
"I don't know exactly what the crisis is - there's no crisis here.
"There's a lot of disappointment, but there's no crisis."
The current winless run is among the worst in the club's history but McGhee rubbished suggestions that kind of statistic would act as motivation for his players on Saturday.
"I would hope that they would want to win the game, as they should every game," he said.
"The fact that it represents a run of games like that, I don't think probably will enter the players' minds."
Defending his side's displays over the last two months, he added: "It wouldn't be 11 bad performances in a row.
"It would probably be six or seven. There are lies, damned lies and statistics. It's where you finish that's the most important thing.
"Chances are, if Lee Miller had stayed, we would've won four points, if not six points more."
Of Saturday's match, he added: "Believe it or not, I am looking forward to it.
"It's a huge test. If we were coming in on the back of 10 wins, this game would be a big test.
"I'm looking for something to give us a bit more of an edge and hopefully a derby game will do that."
The Aberdeen supporters have not held back in venting their frustration at McGhee and his troops in recent weeks and the Dons boss accepts it is up to his players to win them round.
"I think we can create an atmosphere if we make a good start, a positive start," he said. "If we were to get the first goal - for instance - I think the atmosphere would be there.
"Given the run we've just been on, we can't expect the fans to turn up and create the atmosphere without help.
"We've got to earn their respect again."
There was good news to report on the injury front, with Gary McDonald's hamstring strain not the season-ending problem it was first feared to be.
"The scans haven't shown any damage," McGhee said.
"Yet, he's still tender, a little bit sore.
"It looked like a really bad one - like you'd been shot in the back of the leg.
"Hopefully, if he misses this week and next week then he'll be back."