The City boss made three changes from the side who were held to a goalless draw at Stamford Bridge on Sunday, including introducing Mario Balotelli in place of Edin Dzeko, and the striker repaid his manager's faith by opening the scoring midway through the second half.
And substitute James Milner ensured that the points would be heading back to the Etihad Stadium after his stunning strike finally killed Wigan off just over a minute later.
"Yeah, it was [a thoroughly professional job], especially after the first half," Barry told Sky Sports at full-time.
"We found it quite tough tonight, the pitch was tough going and there were a few stray passes. But, in the second half, we ground it out and it was a great three points in the end.
|7/1||Gareth Barry is 7/1 with William Hill to score anytime in Manchester City v Everton|
"When the results go your way, he's [Mancini] the best technician in the world but, if they don't, he's the worst," Barry added. That's just the world we live in, it's football.
"You see a lot of great teams come here and slip up throughout the Premier League and, on last year's results, they are vital points that came our way. Hopefully come the end of the season they will be a big three points."