Wilson's strike after 53 minutes, bending a lovely effort past keeper Simon Sluga and into the net from outside the box, was followed up by Will Vaulks' effort just three minutes later, proving too much for the Hatters.
McCarthy, who has now won four in a row since replacing Neil Harris in the hot-seat, said: "It wasn't a particularly pretty game of free-flowing football.
"We didn't start the second half well but Harry got a bit of space and punished them with a wonderful goal.
"There wasn't long between the two goals and they had an uphill battle after that.
"It has been a big bounce. I have had a really good response from the squad and let's hope it continues.
"I just know this league, it can turn around very quickly, so there will be nobody getting their feet off the ground."
After a first half that saw Luton have the better chances, James Collins and Danny Hylton both sending headers wide from close range, City's quickfire start to the second period was to prove decisive.
Wilson's curler set them on their way, as he was denied a second by a brilliant Sluga save, but the resulting corner saw an unmarked Vaulks double the advantage via a slight deflection.
Luton never gave up though and should have pulled one back midway through only for midfielder Pelly Ruddock Mpanzu to slice wide from inside the box.
Harry Cornick then had an effort deflected off target late on, as a frustrated Hatters boss Nathan Jones said: "I'm disappointed, I thought first half we were very good, we matched them all over had the best chance through Collo, then we had to reshuffle (with an injury to Tom Lockyer), and that derailed us completely.
"They were able to have a knockdown without anyone around him and then he (Wilson) scores from 25 yards, so that was it really and I'm really disappointed as we switched off, we didn't do the basics right.
"We wanted to make sure we were right at it and we were for pretty much 50 minutes, but when you switch off and a side that's in good form and has good players then that's what happens.
"We're disappointed, but we need to be better, we need to be more clinical when we have chances and a real disappointment we had to reshuffle and then got derailed."