The Pittodrie boss even encouraged his players to criticise his own performance since he took charge last summer and goalkeeper Nelson reckons the summit could prove a turning point in a campaign that is in danger of unravelling.
"People got things off their chest," said Nelson, 28.
"It gave everyone an opportunity to speak.
"What was said will remain in the dressing room and it'll bring us closer together."
McGhee was spat at as he left the field after Tuesday night's shock Active Nation Scottish Cup fifth-round replay defeat by Raith, which came just three days after a stirring fightback secured a 4-4 SPL draw with Celtic.
Nelson, who had a scarf tossed at him by travelling fans at Falkirk Stadium, added: "You don't become a bad team overnight and this is the team that drew 4-4 with Celtic, the same team that beat Rangers this season."
Asked what was causing the inconsistency which has now seen the Dons go seven matches without a victory, Nelson said: "If someone could put their finger on it, I think we'd win every single game.
"We want the fans to back us, and we know the only way the fans are going to back us is if we do well.
"It doesn't matter how much stick we get because we're hurting and we want to win games."
Saturday's game was one of mixed emotions for Nelson, who was playing almost two years to the day after his last competitive appearance.
The summer signing from Norwich had not kicked a ball in anger since starting Leyton Orient's 1-0 home defeat by Nottingham Forest in February 2008.
He told RedTV: "On a personal note, I'm delighted, because I always wanted to pull on the Aberdeen shirt since I signed for this club.
"The result is disappointing for me and the team and everyone involved with Aberdeen Football Club but it doesn't take any gloss off the fact that I've made my debut."
Nelson was drafted in for Jamie Langfield against Falkirk and McGhee is now considering giving him a run in the team.
Yet, the Dons boss insisted Langfield had not been made a scapegoat for the Raith defeat.
He also revealed Jim Paterson would miss Saturday's game with Hearts with an Achilles injury that forced him from the field.
Aberdeen came unstuck against Falkirk largely through their inability to handle Enoch Showunmi, who had a hand in all three of his side's goals.
The January signing from Leeds looked unplayable at times and capped an outstanding display with a stunning scissor kick, his first goal in Scottish football.
"Not one I normally score but I think I've probably taken a little bit out of Peter Crouch's book," joked the 27-year-old, who admitted the strike was up there with the best of his career.
"A couple of my other performances deserved goals but it didn't happen so it's just great to get off the mark."
The win was Steven Pressley's first in management and the performance was arguably Falkirk's best of the season.
It closed them to within a point of safety ahead of Hamilton's game at Hearts on Sunday.
Showunmi added: "The lads that we have here and the attacking players we have here are well equipped to get off the bottom of the table.
"More performances like that and a bit of luck along the way will help us achieve that."
Source: Team Talk