The Czech playmaker cracked home a superb goal after just 72 seconds at Tottenham on Sunday, which proved enough to win the north London derby despite plenty of pressure from the home side.
Wenger will take charge of his 1,000th match at Chelsea next weekend with his side back to within four points of the leaders, on whom Arsenal also hold a game in hand.
The Gunners, though, remain outsiders for the championship, as Manchester City are expected to go clear at the top having played three less, while Liverpool, currently second on goal difference, impressed after a 3-0 romp at Manchester United.
Rosicky, though, stressed confidence was high within the Arsenal squad, who produced the perfect response following the disappointment of a midweek Champions League exit to Bayern Munich.
"You cannot influence what the people around you are saying. I mean no disrespect to you (media), but I absolutely don't care what you are saying - don't take it negatively, but it is like that," Rosicky said.
"Only what counts is that you come to the pitch and win the game, if you don't win the game, obviously you are right.
"The only thing that you can influence is on the pitch, the truth is on the pitch, nothing else matters."
Rosicky added: "Since I have been in England and playing for Arsenal, it is the first time it has been like this, with four teams basically fighting for the title.
"You can see how unpredictable it is - we lost at Stoke (last weekend), Chelsea lost at (Aston) Villa (on Saturday), so every game is very important for everyone.
"It can change very, very quickly in two games and of course you talk about Chelsea and Man City, but you have to talk about Liverpool also."
Arsenal could have been further ahead before half-time in the derby, but both Alex Oxlade-Chamberlain and Lukas Podolski missed good opportunities.
Spurs also had their chances and it took a superb goalline block from defender Laurent Koscielny at the start of the second half to stop a point-blank range effort by home midfielder Nacer Chadli after a handling error by Wojciech Szczesny.
Arsenal, though, could have had a penalty when Koscielny was bundled over by Jan Vertonghen before Hugo Lloris saved Per Mertesacker's low shot.
Rosicky, 33, believes this season the Gunners have all the ingredients to finally end their long trophy drought, with an FA Cup semi-final against Wigan also to look forward to.
"When we were 1-0 up in the past, sometimes these games slipped through our fingers," said Rosicky, who joined Arsenal from Borussia Dortmund in 2006 and recently penned a contract extension.
"This time, you could say the defence was outstanding - the two centre-backs were excellent, but on the other side as well, I think we have plenty of improvements offensively [to make] because there were so many moments in some situations when we could have played much better and we would have closed the game earlier.
"But maybe in the past we would not have won a game like that."
After facing Chelsea, Arsenal host Swansea next Tuesday night and then Manchester City on March 29.
Gunners boss Wenger is expecting a tense run-in for all concerned.
"We wanted to get back in the race and the defeat of Chelsea, the win of Liverpool and of Man City away makes the final sprint very interesting," he said on Arsenal Player.
"It is not in our hands because even if we win our game in hand we are still a point behind, but if we continue to win our games that will of course be very important, then it is in our hands.
"(Afterwards) then it is just focus, recover, focus and try to win the next game."