The midfielder was sent off in the first half after stretching to reach the ball in the Everton penalty area and then colliding without Jordan Pickford.
Referee Chris Kavanagh gave no foul but the Video Assistant Referee, Matt Donohue, recommended a red card and Norgaard has given his marching orders.
Bees manager Thomas Frank after the game - which ended as a 0-0 draw at Goodison Park - confirmed the club would appeal the decision.
"For me it is not a red card," he said, before adding: "“The ref has been told to take on-field decisions, which in my opinion was a good on-field decision but was overturned by VAR.
"If VAR is told studs on leg is a red card then we need to be told and that has to be consistent going forward – very, very consistent going forward.
"If it is not the law or the rule then Chris (Kavanagh) was not brave enough to overturn the situation.
"On top of this, there were several Everton players who were saying: ‘That is not a red card’. We will most likely appeal this.
"We need to find out if that is the law going forward and if it is not then the \[disciplinary commission\] have to overturn it and if they don’t overturn it, they also have changed."
The Football Association announced on Wednesday morning that Brentford's appeal was successful, making Norgaard available again for selection starting with Saturday's visit of Leicester City.
"Christian Norgaard will be available for Brentford's next three matches following a successful claim of wrongful dismissal.
"The midfielder was sent off for serious foul play during the Premier League match against Everton on Saturday, 23 November."
Create a FREE account to continue reading
Registration is a free and easy way to support our journalism.
Join our community where you can: comment on stories; sign up to newsletters; enter competitions and access content on our app.
Thank you for registering
Please refresh the page or navigate to another page on the site to be automatically logged in