Arsenal have not lifted a trophy since the 2005 FA Cup final, which was played in Cardiff.
Rosicky, who joined from Borussia Dortmund in the following season, believes another piece of silverware is long overdue.
"It is important to end the trophy drought because we haven't won anything for a long time. You can see the boss is going for it," said the 29-year-old.
"He wants to win the Carling Cup more this season because he took the whole team here. That gives us a better chance of winning it, we have a good enough squad to compete on all levels.
"I came in 2006 and have won nothing yet. I came here to win trophies, so let's go for it in style."