The Pittodrie club announced on Wednesday night they had parted company with McGhee, along with assistants Colin Meldrum and Scott Leitch and confirmed plans are now underway to find their next manager "without any timescale being set on the appointment".
Aberdeen Supporters Trust spokesman Jeremy Wood told Press Association Sport: "The key thing now, whether it's an interim arrangement or a permanent appointment, is getting someone in who will bring stability to the club, get results and get us away from the bottom of the table."
He added: "What the fans will be concerned about now is landing one of the usual suspects which are always bandied about. The likes of John Hughes and Terry Butcher would not be popular choices. More popular would be someone like Jocky Scott, even in a mentoring role.
"I wouldn't say he is top choice but the fans will be struggling to get their heads around who is available and who would want the job. There are not a lot of candidates.
"Derek McInnes has done a good job at St Johnstone and Billy Stark was a popular player here in the 1980s, who has done okay with the Scotland under-21s, so they could be candidates."
Of McGhee's departure, Wood added: "I think surprise is the obvious reaction after the board had previously let things go after the Celtic and Inverness games.
"They decided to stick with Mark McGhee then and it looked as though that would be the case at least for the rest of the season.
"I said at the time that decision made the board look a bit indecisive and this confirms it. He was given the proverbial vote of confidence and, a couple of abject results later, he has now gone.
"It's time for a fresh start, although the news will probably be met with mixed reviews. But results have been absolutely dismal. After the Kilmarnock game, I think things just ran out of steam and there was not much more to be gained from things staying as they were."