The Manchester City midfielder hailed his manager's decisions after Mario Balotelli returned to the starting line-up to fire the crucial opening goal at the DW Stadium
The City boss made three changes from the side that was held to a goalless draw at Stamford Bridge on Sunday, 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 the points would be heading back to the Etihad Stadium after his stunning strike finally killed off Wigan 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.
"We have to give them credit. They play a different formation to what we're used to playing against with the three across the back. But in the second half we did step it up, the manager changed things around and the goals came at a great time.
"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."