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.
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."
He added: "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, though, saying: "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."