Arsene Wenger insists he never doubted Olivier Giroud's ability to recover after a difficult week for the Arsenal striker.
Giroud made a public apology to his family and his club after finding himself the subject of lurid newspaper reports about his private life.
Wenger had dropped the striker for the Gunners' last two games, but having been restored to the starting line-up on Saturday, France forward Giroud scored twice in the 4-1 home victory over Sunderland that kept his side within a point of Premier League leaders Chelsea.
And Arsenal manager Wenger said: "I had no hesitation about his strength of character. Of course you want him to come back into the team and be successful, which he was today because he scored two goals.
"One great one at the end of great movement and the other a little bit of a gift from Sunderland. he got an assist as well so he did well."
Wenger was also satisfied the victory restored his side's belief after the midweek Champions League defeat to Bayern Munich.
Bayern's 2-0 first leg victory at the Emirates Stadium left Arsenal facing a daunting challenge if they are to make the quarter-finals when the teams meet against at the Allianz Arena next month.
But Wenger remains confident and said: "Against Bayern Munich the target was to have a good performance and a good result. We only had the good performance.
"Of course we were very frustrated but we had to transfer the positives that we got from this game.
"Overall, we believe we can still have a go at Bayern. We have shown today we are capable of responding and that is the most important thing.
"You see City have a difficult game, Chelsea had a difficult game so you see it is difficult for all the teams at the top, but we did the job well."
Giroud struck twice in the opening 31 minutes before Tomas Rosicky gave the Gunners a three-goal advantage shortly before the break by finishing off a fine move.
Laurent Koscielny made it four in the 56th minute, while Emmanuel Giaccherini scored a consolation for Sunderland in the 81st minute.
Wenger revealed Germany midfielder Mesut Ozil had been left out because of a thigh problem, while Koscielny, Nacho Monreal and Jack Wilshere also picked up minor knocks.
Sunderland manager Gus Poyet was left frustrated by his side's display eight days before they face Manchester City in the League Cup final and admitted his plans for the trip to Wembley had been left in tatters after this display.
"No one put himself in the team for next week. You can say the goalkeeper had nothing to do and that's true." Poyet said.
"You can say Jack Colback tried to go everywhere and tackle and fight and that's true and Fabio Borini, yes that's true.
"But I need to make a team. And whatever team I pick next week has got to be right because they had a great chance to put themselves first and they didn't take it.
"Everything I had in mind for next week is gone in 90 minutes. Gone completely. So we have to start from zero.
"There are plenty of similarities between the way Arsenal and Manchester city play and that gives me plenty to ponder on."