Many have also warned that they must bring some stability to the club or risk a second straight relegation.
Appleton's sacking after just 67 days was confirmed on Tuesday in a short club statement. His predecessor Henning Berg managed 10 days less at the helm before he too was fired.
Indian poultry firm Venky's are now looking for a fifth permanent manager since their £23million takeover of the club in November 2010. Sam Allardyce was the first boss to go, sacked within a month of the buy-out with the club 13th in the Barclays Premier League.
He was succeeded by Steve Kean, who resigned last September following a long campaign of protests from supporters against him.
Rovers are currently 18th in the npower Championship, only four points above the relegation zone.
Wayne Wild, the co-chairman of supporters group the Rovers Trust, said in a statement: "News of Michael Appleton's sacking ought to come as a surprise, but sadly it does not.
"This is just the latest in a long line of incomprehensible and ill-thought out decisions that go back to the very start of the Venky's ownership of Blackburn.
"It is obvious to any experienced fan or football professional that to keep changing managers - we are now looking for our sixth this season - will only lead to yet more instability and uncertainty. It is also a costly exercise to keep paying off staff.
"The owners have to face up to the fact they are entirely responsible for the situation we find ourselves in with a second successive relegation a distinct possibility."
Wild demanded that Venky's start to communicate with fans and other interested parties, and that they ensure the next man in permanent charge has managerial pedigree.
"We've been calling for an experienced manager to be given the job, but they've made three appointments, all of inexperienced managers, and they just aren't learning from the mistakes they're making," Wild told Press Association Sport.
"All our recent success has been with having an experienced, established manager. All our recent failings have been with having an inexperienced manager, and I include Paul Ince and Brian Kidd in that when the club was under the Walker Trust stewardship.
"Kenny Dalglish, Graeme Souness and Mark Hughes have all been successful in their careers, so history tells you what the right decision is."
Wild, a director of the WEC Group, an engineering and fabrication company which is the main sponsor of the Darwen End stand at Ewood Park, has written to Venky's on numerous occasions seeking to set up meetings with the Rovers Trust in an attempt to get fan representation on the club's board.
"Correspondence from Venky's has always been non-existent," said Wild.
"We've tried to correspond with Venky's many times but we've never had a direct reply.
"Again, today, we've had no information from the club. No one knows why (Appleton) has been sacked, what the reasons are or what the plan going forward is.
"It's very difficult to get anything out of the club regarding what's happening next.
"There has been a gulf developing between the owners and supporters for some time now and it's getting worse."
The statement from Blackburn confirming Appleton's sacking read: "Blackburn Rovers FC can confirm that Michael Appleton has been relieved of his duties as manager along with assistant manager Ashley Westwood, first-team coach Darren Moore and head of senior recruitment Luke Dowling."
The Sports PR Company, which represents Appleton, later released a statement from him via Twitter which read: "I am disappointed to be leaving Blackburn Rovers. I would like to thank the players and wish them all the best for the rest of the season. I would also like to say thanks to the fans who have made me feel so welcome over the past few months."