McCarthy's team are among five clubs trying to avoid two relegation spots this Sunday, but have a one point advantage over three of them.
"You never give the dreaded vote of confidence but Mick has been here for five years and I don't believe you get any progress at all by chopping and changing," Morgan told reporters. "Chopping and changing has happened in other clubs and what good has it done them?
"I know Mick has made progress every year since I've been here. There are times in life when things don't go right but you've got to get back up and stand together and make sure you get it right next time."
Wolves face fellow relegation strugglers Blackburn in the clash at Molineux on Sunday. Kickoff is at 16.00.