Ten Hag was shown the door less than halfway through his third season as United manager.
South African great McCarthy was on Ten Hag's backroom staff as a striker coach.
"I was given an incredible opportunity to work with one of the biggest and best clubs in the world under the guidance of Erik ten Hag," McCarthy told BBC Sport Africa. "I learned utmost professionalism because the manager I worked under was not just a disciplinarian, but he was the best and one of the most unbelievable professionals I've ever seen in the game.
"Extremely hard-working, very dedicated, very passionate, he planned on being the Manchester United coach for the next 10 years. That was his vision."
McCarthy also defended Ten Hag's record at Old Trafford.
He continued: "Everyone is talking about how bad, how terrible Manchester United is.
"We still managed to win the FA Cup, we still managed to win the Carabao Cup. I was proud that I was part of that regime.
"Honest to God, I don't know what the issue is. It is just such a huge football club and the problems just seem to go on and on - and I don't know how they're going to resolve it."