The Gunners' 2-0 win at Bournemouth was their first in five league games and moved Wenger's side up to third place, five points adrift of Leicester before next weekend's meeting between the two teams.
The Arsenal manager believes it was crucial his side ended their dismal recent run but is convinced they will now meet Claudio Ranieri's side with renewed belief.
“Yes, of course (we needed a win), for two reasons. One we haven't won for a while, we had four games without a win,” said Wenger.
“When you play at the top, that's a long period, confidence drops a little bit. Leicester running away and us playing them next week, to make the game interesting, it was very important for us to win today.
“In one week, Leicester has beaten Liverpool and Man City. So that means suddenly they become the favourite in the league. That makes our game on Sunday a very big one.”
He added: “We have been in a title race and we are still in it. We cannot control people's opinions.
“We can just control our performances and to show that we believe in it, you know, and that we have the level to do it. There's still a very long way to go.
“I agree with you that Leicester now are the favourites. We have a big game at home now against them, and I believe we have enough quality and nerves to deal with that.”
Arsenal went into Sunday's game having failed to score in their last three league outingsa but secured the points through first half goals from Mesut Ozil and Alex Oxlade-Chamberlain.
Wenger believes his side's performances have not been getting the rewards they deserve but admitted his relief at claiming all three points.
“I think we needed to win the game. I do not want to be too dramatic with making statements. A football game away from home in the Premier League for anybody is difficult to win. We had to win. We won.
“In our last three away games, we played Liverpool, equalised in the last minute, we played at Stoke, 0-0, and we came here today, and won, so I believe that we have shown good performances.”
Ozil again impressed, capping a fine all-round display with a goal.
“He has become a very important player, I think he has added fighting attitude. It was a top performance again,” said Wenger of his influential German star.
Bournemouth manager Eddie Howe was convinced his side's chances were dented by the failure of referee Kevin Friend to dismiss Mathieu Flamini for a foul on Dan Gosling.
The Arsenal midfielder was punished with only a yellow card but Howe said: “I felt it was a red card. Had a very good view and thought it was two footed. That kind of tackle has been outlawed.
“You can't do it. It was a straight red, a simple decision. I was surprised when referee only produced a yellow.
“I haven't seen a replay but it was two-footed and Dan could've been seriously injured on another occasion. That's why I thought it was a straight red. It didn't look like it was under control.”
But Wenger took an opposite view.
“I didn't see it like that, honestly I felt even at the start it was free-kick for us,” said the Frenchman. – AFP
Original source: Leicester are title favourites - Wenger