Neil Warnock was sacked as manager of fellow strugglers QPR earlier this week while Blackburn boss Steve Kean has come in for constant abuse from the club's supporters.
But Morgan and Wolves chief executive Jez Moxey have constantly shown their support for McCarthy during good and bad times and nothing has altered despite the current Premier League survival fight.
When asked about Warnock's dismissal, Morgan said: "It's not for me to comment on other clubs. All I can do is comment on Wolves and we do not have a hire-and-fire mentality.
"Of course, we have problems but our philosophy is to work through the problems.
"This club is about stability and approaching things in a very business-like sense.
"Of course, we want the team to do better than it is currently doing. But you don't get long-term growth by chopping and changing all the time."
Morgan added: "The message is finally dropping with people that this is a club about stability.
"You don't get stability by chopping and changing your manager all the time.
"You have to work things through. I'd like to think football thinks Wolves do things our way - and our way is about long-term growth, stability and strength.
"You get strength from teamwork."
Morgan stopped short of giving McCarthy the dreaded vote of confidence but insists that has always been his philosophy even through successful times at Molineux.
He said: "I've never commented on the manager's job in four-and-a-half years I've been at the club and I'm not going to start now.
"That is part of the stability if you like, that you never get the dreaded endorsements and the 'votes of confidence'.
"I never gave it when we won the Championship so it's not a case of doing it in good times or bad times. It's never."
Morgan was speaking at the unveiling of details of new hospitality facilities in the Stan Cullis stand which is currently being rebuilt.
It will incorporate new restaurants, a gastro bar and a club museum.
The lower tier of the £18million stand, housing 4,000 seats, is already open with the top tier, which consists of another 3,700 seats, set to be ready for the start of next season.