The 2-1 victory at QPR on Saturday ended a nine-game winless streak and saw the Black Country club climb out of the relegation zone.
And McCarthy told the club's official website: "Can I just say something about my owner? We have won three games in 22 and I am still here as the manager of Wolves."
He added: "Let me tell you that is some level of support so let's not forget that.
"When everyone is writing negative stuff about me and Steve he has been as supportive as anyone else.
"I owe him a debt of gratitude for that."
Much had been made of the visit by owner-chairman Morgan to the players' dressing room after last week's 3-0 home defeat by Liverpool.
McCarthy maintained that matter had been "sorted out" quickly and, after the win over Rangers, the Wolves manager highlighted the support he has from the boardroom.
Wolves host local rivals West Brom on Sunday and are awaiting the results of tests to a knee injury for on-loan Arsenal midfielder Emmanuel Frimpong.
Source: PA
Source: PA