And McGhee admitted his players could become victims of a cup upset if they perform in a similar vein against Raith Rovers at Stark's Park in the fifth round of the Scottish Cup on Saturday.
He said: "I have spoken to the players about Saturday already. I am not prepared for them to go to Raith Rovers and play like that.
"I told them that Raith Rovers will have seen that performance and taken huge encouragement from what they have seen. They will be thinking that if they get in our faces on their own pitch they can beat us.
"Had they been at Tynecastle last week they may have packed their bags and gone home. But now we have showed them that they have a chance so we are going to have to improve in lots of ways if we are going to have any chance of beating Raith Rovers."
McGhee also said he was delighted to hear that Dons striker Chris Maguire, who has joined Kilmarnock on loan until the end of the season, scored the winner for his new club against Celtic.
He added: "Chris Maguire wasn't making a contribution here and what he needed was a fresh start. He has gone to Kilmarnock to get that and clearly it has worked as he has gone there and scored a goal that he hasn't looked like scoring.
"Make absolutely no mistake, I am thrilled for Chris Maguire. Don't think for a minute I'm thinking it is a nightmare. I'm delighted and I hope he keeps doing it and then comes back next season and does it for us."
Falkirk boss Eddie May praised the inspirational performance of captain Darren Barr as his side secured a first victory in Aberdeen since 1958.
Barr has signed a pre-contract deal to join Hearts in the summer but May thought his skipper was excellent at Pittodrie.
He said: "He has been like that for the majority of this season. He has absolutely nothing to prove to anybody. He is going to a very good football club. He could have gone to Aberdeen but it was a personal decision. Darren will be fully committed to the football club and I think he has shown over the last few games what Falkirk means to him."
May admitted his players still have a huge task ahead of them to ensure their top-flight survival.
He added: "We are off the bottom of the league but all the hard work is ahead of us. I appreciate what a hard job it can be as a footballer sometimes, especially if you are not at the top where everything is going great. It is hard being at the bottom.
"I'm sure the players will try their best from now until the end of the season to get Falkirk out of their current situation."
Aberdeen 4/5, Raith Rov. 13/5, Draw 13/5
Source: Team Talk