A home defeat by Watford in the FA Cup quarter-finals last Sunday, followed by a predictable Champions League exit in Barcelona had put Wenger's under-performing side, and his own position, under intense scrutiny.
But goals from Danny Welbeck and youngster Alex Iwobi, on his first league start, sealed a first league victory in four to leave the Gunners 11 points behind leaders Leicester City with a game in hand.
"I'm pleased that we responded under pressure (after) the character of my players was questioned. If we didn't win today, we knew that we were out of it (the title race) so it was a mental test for the side," Wenger told reporters.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"We are today with our backs to the walls and we responded well. In England, it is very hard to give a fair assessment of the performance because when you lose, you are disastrous.
"We have not been as bad as people have said, but I agree that you either win or lose in sport."
Arsenal's display begged the question as to how they find themselves so far behind Leicester, who won 1-0 at Crystal Palace.
"We have to be humble and fight in every game like we did today. Then we never know," Wenger said of the title race.
Arsenal could have scored more had their finishing been a little sharper, although Iwobi, who has been with the club since he was eight, was blameless after his cool finish put the visitors in complete control.
"He is an intelligent boy who is passionate about the game and wants to learn," Wenger said. "Month after month, he developed very well and that is why I integrated him and played him."
(Reporting by Martyn Herman, editing by Alan Baldwin)
