Second-half goals from Mario Balotelli and James Milner allowed the reigning champions to stay within striking distance of league leaders Manchester United and it was the fighting qualities of the City side which impressed midfielder Barry the most.
"We found it quite tough going in the first half, we had some stray passes but we ground it out in the second half and that's a great three points," Barry told Sky Sports.
"Credit to Wigan, we had to change things to get past them.
"A lot of teams come to Wigan and don't get results. These are vital points that have come our way."