The former Scotland boss has overseen a difficult campaign so far having secured just one win from nine outings.
The Dons, who are the lowest scorers in the SPL, are second from bottom in the table just a point clear of Inverness.
Speculation has been mounting that Aberdeen could opt for a change at the helm and part company with Brown and Archie Knox.
However, Miller has quashed the talk, stating that Aberdeen are known for their history of supporting their manager through thick and thin.
"Fans should ignore any talk of Craig being under pressure and in danger of being sacked," commented Miller.
"It's a load of scaremongering nonsense. We have a history of supporting managers through good times and bad and that will remain the case.
"The last week or so hasn't been pleasant whether you are a fan, director, manager, player or one of the many other people working tirelessly behind the scenes at Pittodrie.
"What we have always done in times of adversity is band together and make a united effort to improve our situation.
"Others have talked of Craig being under pressure, not us. He and Archie Knox are the most experienced managerial team anyone could have.
"We have total trust in them eventually delivering the winning Aberdeen team that we all yearn for. It's not as if their careers are full of periods like Aberdeen are going through at the moment.
"They are men who have known only success and you can be sure they will be determined to make the next few weeks more enjoyable for the Dons fans than the last few have been.
"It's time to look forward and concentrate on what can be done to improve our position in the SPL and get the team ready for an assault on the Scottish Cup in the New Year.
"None of us are happy to see Aberdeen sitting in second bottom spot in the SPL after nine games. It's not where we want to be and it's certainly not where we expect to be at this stage but it's a retrievable situation."
Source: Team Talk
Source: Team Talk