After a goalless first-half, Sanchez struck his 20th league goal of the season to put his side ahead in the 60th minute of the match, goal.com reported.
"That's Alexis, you know".
And after the winning performance, Wenger insisted that he had never doubted the character of his players, many of whom have been vociferously criticised by both the press and even the club's own supporters. "He is always tricky to stop, very good in a short space once he has the ball in the box".
"Overall it was a very convincing win", he told Sky Sports. Alexis Sanchez has been poor for the past month, yes he scored in games against Middlesbrough and Manchester City but he didn't play particularly well in either and has looked a player just hoping for the season to end.
Realistically, we need Liverpool to drop points in their last two games and Arsenal to win all four of our remaining fixtures to take fourth, so we simply can't afford to slip up tonight.
Wenger on Perez's lack of first-team opportunities: "He's a top-quality striker and I couldn't give him the games that he wants and that he deserves".
With six minutes left, Arsenal made sure of the points when Sanchez and Ramsey combined to set up Giroud, who had the relatively simple task of heading home from close range.
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Wenger called on members of his squad to make an impact when called upon. "It's hard for me at the moment, it's between Welbeck and Giroud".
"I'm always harsh with the one that doesn't play".
"We were focused and I felt that when we suffered we stuck together", he said. "We were dynamic, quick going forward and well-organised". But that is a good opportunity to show your character - to show how you come back and how you recover. But I think we can do a good game against this team - to keep, of course, a good structure, to defend together and to prevent them chances.
"We'll need another strong performance at Stoke. So let's just continue".
Arsenal moved above Manchester United into fifth on 66 points.
Arsenal's Olivier Giroud, left, celebrates scoring his side's second goal with Aaron Ramsey during the English Premier League soccer match between Southampton and Arsenal at St Mary's stadium in Southampton, England, Wednesday, May 10, 2017.
"He came off with a tight hamstring, and we'll know maybe in the next 48 hours how bad it is", he said.
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