Wolves dropped into the Barclays Premier League's bottom three on goal difference after Peter Odemwingie hit the second hat-trick of his career for the visiting Baggies at Molineux.
A section of Wolves fans vented their anger at the directors' box towards the end of the game and a couple of hundred protested afterwards by the Billy Wright statue.
McCarthy said: "I would think it was one of the most disappointing afternoons of my career.
"I apologise for the performance and I've never done that before. But the way we capitulated in the last half-hour is not associated with my teams."
When asked if he was still the right man to lead Wolves, McCarthy said: "I always feel I'm the right person to do it.
"I've not got a message for the fans. I've apologised. That is all I can do. That's how badly I feel about it."
McCarthy was unhappy with his side's performance even though they came in at half-time at 1-1.
He said: "We came here on the back of a good win and performance at QPR last week. We got away with the first half and started the second period well.
"But we did not deal with two corners which cost us and then at 3-1 West Brom picked us off when we pushed forward."
Baggies boss Roy Hodgson believes McCarthy should remain in charge at Molineux.
He said: "I think Wolves will stay up if they keep their heads because they have an outstanding manager and an outstanding owner as well.
"I feel sympathy and empathy for Mick a because we're both experienced coaches. At the risk of sounding arrogant, I think Wolves can be more than satisfied with what Mick has done for the club.
"I think he's done an excellent job and continues to do an excellent job.I 'm always saddened that those jobs don't always get recognised.
"But on the other hand I don't want to appear naive. I know it's part of the game nowadays and it doesn't matter whether you're God Almighty or Mick McCarthy, people are going to think there's people out there who can do it better.
"My final comment on the subject is that people should be careful what they wish for."
Hodgson praised Odemwingie's treble, with Jonas Olsson and Keith Andrews also on target for the Baggies.
He said: "Peter's season's been a bit stop-start and that's not good for any player.
"Why he's doing so much better now is because he's training every day, he's playing every weekend, he's getting into a rhythm that every player needs."
Steven Fletcher's 10th goal of the season provided Wolves' consolation effort.