Shiels begins a three-match touchline ban at Pittodrie on Saturday after his latest appearance before a Scottish Football Association judicial panel.
The Killie boss was given an immediate two-match ban for comments made regarding referee Euan Norris after he sent off goalkeeper Cammy Bell in a defeat by Inverness in November.
Shiels also saw a suspended one-match ban come into play for comments made about a referee last season but escaped further punishment for his recent dismissal against St Johnstone.
Brown is reluctant to comment on decisions by match officials and he feels 56-year-old Shiels will naturally follow suit.
The 72-year-old said: "You get a bit immune to pressure as you get older.
"Kenny's fairly recently come into management in Scotland. He's a bright, lively, intelligent guy but in 15 years from now he won't be quite so exuberant. He'll calm down a bit.
"You see the likes of Sir Alex (Ferguson), when he was here he would have fought anyone. He would have fought ball boys if necessary, the crowd, the referee, but he is calm now.
"I can see there have been some controversial decisions but we have all had that.
"The route to take is through John Fleming, the head of refereeing. If I have got anything to say I send an email or phone John Fleming and I always get a response. I say it confidentially but never publicly because referees don't like public criticism."