Czech winger Rosicky captained a strong Gunners team which beat Tottenham 4-1 after extra-time at White Hart Lane last night.
Manager Arsene Wenger - watching from the stands as he served a one-match touchline ban - selected a balanced squad, with Henri Lansbury, who opened the scoring on 15 minutes, the only reserve-team youngster to make the starting XI.
Wenger has said the Gunners will continue with the selection policy in a bid to reach Wembley, should he not see his options further depleted by injuries, with full-back Kieran Gibbs now sidelined for a few weeks by what was initially feared to be a serious foot injury.
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."
Robbie Keane had drawn the home side level just after the restart, and neither team was able to find a winner in normal time.
However Arsenal went back in front at the start of the first period of extra-time when Samir Nasri slotted in a penalty after being tugged back by Sebastien Bassong, before the Frenchman added another from the spot four minutes later following Steven Caulker's foul on Marouane Chamakh.
Andrey Arshavin scored a fourth to silence the White Hart Lane crowd.
Rosicky, who missed a crucial penalty at Sunderland on Saturday, admitted he was somewhat taken aback by the squad selection, which also included a strong bench.
"I was happy I was playing because a game against Tottenham is a great one to play in," he said.
"Maybe I was a bit surprised that the whole team came here even though he rotated a little bit, but all the players who played in the starting XI last night showed that they are ready and want to play."
Teenager Jack Wilshere continued his progression with another impressive display, which Wenger hailed as "outstanding".
Rosicky believes the 18-year-old, who won his first senior England cap at the start of the season, takes everything in his stride.
"He is a great talent. For his age, he has a great brain and a big future," said the Czech international.
"When Jack has got the ball, he is very calm. That is something young players sometimes don't have, they panic a little bit.
"With him you don't see it because he is very comfortable with the ball and that is the first quality you are looking for."
Arsenal today confirmed Gibbs' injury is not as bad as first feared.
The left-back missed a large part of last season because of a broken metatarsal, and with it the chance to feature at the World Cup.
Today's scans have revealed nothing more than severe bruising, but no definitive timescale has been set for the 20-year-old's return.
Arsenal are already without captain Cesc Fabregas, England winger Theo Walcott, Holland striker Robin van Persie, Denmark forward Nicklas Bendtner and midfielder Abou Diaby because of injury.
However, centre-back Thomas Vermaelen could be available for Saturday's home match against West Brom after his Achilles problem.
Fabregas, meanwhile, knows this is a big season for him, the Spain international fully committed to the Gunners cause following a summer of speculation over a move back to boyhood club Barcelona.
"I am completely focused, I know what I want to do and what I have to do. My mind is centred on what happens on the pitch, which I enjoy," Fabregas told Spanish radio station Cadena COPE.
"If I could not play football then I may worry, but while I still can here or wherever I can say I am happy.
"I am at a great club, in a great team and I want to do the best and have a great year."