Rosler's side, who have a Wembley date with Arsenal to come next month, had dropped two league points in midweek after conceding a stoppage-time equaliser against Yeovil.
But the FA Cup holders got back to winning ways with a home win their manager reasoned was entirely merited.
Lewis McGugan gave the Hornets the lead against the run of play after 36 minutes.
But Wigan were back on level terms within four minutes through Jean Beausejour's header, and the points were secured when Martyn Waghorn rifled home 10 minutes into the second half.
"We had the majority of the possession and far more attempts on goal," said Rosler.
"Even before they scored, we had three massive chances - two of them one-against-one.
"I felt we were very unfortunate to go a goal down, but we had to sort out one of two things defensively.
"We did that in the second half and, apart from the last 10 minutes when they changed their shape and went more direct, I don't think they caused us many problems.
"We didn't panic when we went 1-0 down, we carried on playing, and I felt we had chances in the second half to kill the game off completely.
"With the match programme, we are looking a little heavy, and we could have done with the two-goal cushion.
"But overall I am very happy."
Visiting boss Giuseppe Sannino was proud of the way Watford fought right to the end, despite extending their winless run on the road to 14 matches.
"When I lose I am always disappointed," Sannino said.
"But I can say my lads gave everything in terms of effort, spirit and commitment.
"Let's not forget we were playing a very good side, and we gave a good account of ourselves.
"I can see some positives from the performance. The lads showed me something more."
Sannino felt Watford paid a high price for conceding the equaliser so soon after going ahead.
"It would have been an advantage to have gone in 1-0 up at half-time," he added.
"But the mistakes we made allowed Wigan back into the game.
"We created our own problems at times, and I am disappointed with that."