Johnson says the players should take responsibility for the current dismal run of results.
Tuesday night's 3-0 home defeat to Liverpool means Wolves have gone nine Premier League games without a win and collected only four points during that period.
Fans vented their anger towards McCarthy at the final whistle and one banner proclaimed "Mac Out" but Johnson believes changing the manager is not the solution to Wolves' current plight.
Johnson said: "Mick is still the right man. Changing the manager isn't going to change what the players do on the pitch.
"Unfortunately, that's what it's like in football. The manager's head is on the chopping block. It's unfortunate.
"For me and all the lads, the manager needs to stay. We respect the manager massively.
"He's the man to get us out of it, he's done it before and he'll do it again. He's a fighter. You can't really get a better man for the job."
Johnson, who was relegated with Birmingham last season, added: "We've let ourselves down. The players on the pitch are the ones who let the staff and the fans down.
"We let ourselves down but it starts now again with Saturday at QPR. It's a massive game and a must win game. We'll all be up for it."
Second-half goals from Andy Carroll, Craig Bellamy and Dirk Kuyt doomed Wolves to defeat and kept them in the bottom three in 19th position.
Johnson said: "In the first half there was no danger. In the second half, we conceded a goal and it was backs to the wall after that.
"We found it difficult to get near them, they were playing around us.
The goal killed us. It was one of those nights when we needed to keep a clean sheet. They did us on the break. That's what Liverpool do."
Wolves chief executive Jez Moxey had re-affirmed his support for McCarthy in his programme notes for Tuesday night's game.
He said: "Falling into the bottom three sometimes seems to bring with it additional psychological baggage and we are well aware of disappointment amongst fans at our position in the table.
"We are aware of supporters' opinion and feedback but we are also able to make decisions on all club matters in a calm and considered manner, doing the best for Wolves in the short and long term.
"No-one should forget where we were when Mick McCarthy took over and the enormous progress we have made and the tremendous progress since Steve Morgan (club owner) invested so much money in the club.
"We were in this position last season and the management and players came good and it is by all sticking together and remaining positive that we have the best chance of doing so again."
