The Czech Republic midfielder scored twice as the Gunners dispatched West Brom at the Hawthorns on Saturday but acknowledged they must gain consistency on home turf
Rosicky scored twice as Arsene Wenger's team defeated West Brom to move within two points of Chelsea and Tottenham, who currently occupy third and fourth place respectively, with a game in hand on the latter.
Arsenal are in a rich vein of form, having won six of their last eight in the top flight, but the 32-year-old claims further improvements are needed on home turf if they are to qualify for the Champions League.
"During the last couple of games we have produced some good football," Rosicky told the club's official website after victory at the Hawthorns.
"It gives you confidence when you win in Munich and at a place like West Brom when in the last 20 minutes your backs are against the wall.
"But if you are speaking about third or fourth place you have to win your home games. Our form there must improve.
"If you go back and analyse well the game against Tottenham that was not a bad performance. We made two stupid mistakes and we were punished for them.
"We tried to correct them and you could see the improvement in Munich."
Arsenal had already sealed three points on Saturday when Tottenham faced Everton later that weekend but Rosicky insisted that the Gunners did not pay attention to the result of their rivals.
"We are in a position where we just focus on ourselves now," he added. "It is tricky to think all the time 'where are Tottenham and Chelsea playing?' We just concentrate on ourselves and what we are producing.
"We have the experience [of coming from behind to finish third] last year. The team knows the situation that could be [to] our advantage. But as well we know we have to be more consistent.
"And if we produce football every week like we did on Saturday then I am confident we will get there."