McGhee was responding to comments made by Dons legend Joe Harper, who launched a scathing attack on the current squad in the wake of their Co-operative Insurance Cup exit to Dundee.
Aberdeen were dumped out of the tournament by the First Division side in extra-time after fighting back from two goals down.
"I think it's a ridiculous statement," said McGhee. "We lost a game the other night, not because anybody 'bottled it'. In fact, quite the opposite.
"At 2-0 down, that was the time when people were going to 'bottle it'. Instead, they got together as a group, they got in about it and they got themselves back to 2-2.
"We lost a game that we shouldn't have lost. But it was nothing to do with 'bottle'."
And McGhee insists he has no intention of wielding the axe ahead of Saturday's SPL game against Rangers.
He said: "You look at the squad and there is not a great deal of scope for change. The team that finished won't be far away from the team which starts at Ibrox.
"We will put out a team who we believe can win the game at Ibrox. There is no problem with the spirit.
"The boys were in good form this morning, they are all looking forward to the game.
"It's a great place for the young players to go and play and I'll be determined that they should go there with no fear whatsoever."
McGhee - who took over the Dons hot-seat in the summer - admits Aberdeen are nowhere near their best yet but insists results so far this season are far from a cause for concern.
"People create a mood around us and around me," he said.
"It's not my style. I will never allow any sort of depression to set in around the place.
"It's ridiculous. We are only a couple of games into the season. We beat Rangers tomorrow and we are on the same points. It's a great incentive.
"Hibs are playing Motherwell and, if they draw and we win, we go third. We have not even started yet.
"These are teams who are professing themselves to be in good form, to have started the season brilliantly.
"We've not, we've not got playing at all, we've not found any rhythm, a style of play and yet we could be above both of them.
"That, for me, augurs well for the coming months and for the future."
Aberdeen have not won at Ibrox since 1991 but McGhee sees no reason why the statistic should be a source of irritation for himself personally.
"I've not been here during that period," he said. "What is a source of irritation for me is that I've been back in Scotland for two years and I haven't beaten Rangers yet.
"I've had three or four draws but not actually won a game. I've beaten Celtic, I've taken points off Celtic, but I've not beaten Rangers.
"As much as I love Ally McCoist and Walter Smith, I'd like to get one over on them.
"The 18 years before that is really irrelevant. The last time they won, I don't know who was playing here, I don't know what the team was.
"But we have a team tomorrow who, if they play as well as they possibly can play and Rangers don't, can win at Ibrox."