England international believes Gunners are experienced enough now
The barren spell has prompted manager Arsene Wenger to reassess the importance of the competition after he selected several of his first team for their win 4-0 against Newcastle United on Wednesday night.
And that has pleased Walcott, who told the club's official website: "This is a great opportunity for us to win the Carling Cup. We want to win trophies.
"People might say it's the Mickey Mouse cup and stuff like that but for me, personally, it's a trophy.
"Our fans have been desperate for us to win a trophy and the players have as well.
"Hopefully we can win the Carling Cup and it will be one of many.
"If we continue to play football like that it's looking bright for us.
"We take every game seriously but we're getting better with the experience we have now.
"To win 4-0 at Newcastle is a great confidence booster."
It was the 21-year-old England international's first start since early September after recovering from an ankle injury.
Walcott's finishing has been criticised in the past, but he notched a double in the win and hopes he may be beginning to win over the doubters after striking five goals in six appearances this season.