The future of the veteran Dons boss has been the subject of much speculation in recent weeks, with his contract, and that of assistant Archie Knox, set to expire in the summer.
There have been suggestions that the Aberdeen hierarchy may look to bring in a younger boss to replace the duo.
However, despite a poor recent run of results, Anderson believes there is no need for upheaval and would like to see Brown and Knox continue their reign at the club which began in 2010.
"I still believe Craig is the right man to take the club forward," said the former Scotland stopper. "But it is not my decision. We know our form has been patchy, at best, and that is something we are aware of.
"That makes the result against Hibs all the more frustrating because I thought we were the better team."
The case for continuity at Aberdeen has not been aided by the untimely malaise of the Dons. Brown's charges have not won a Clydesdale Bank Premier League match in four outings and, this weekend, exited the Scottish Cup at the fifth round stage after a 1-0 defeat at Easter Road.
A visibly dejected Anderson expressed his disbelief after the loss in Leith - an encounter that saw Hibs goalkeeper Ben Williams steal the show with six fine saves, including a late penalty stop to deny Scott Vernon.
"I just cannot believe we have lost that game," Anderson continued.
"I thought we were the better team, had numerous chances to score, but did not do that. Hibs had two shots and we are out of the cup - that is the harsh reality of football."