The Serbian came off the bench in the 4-0 victory against Wigan Athletic, soon after arriving from Spartak Moscow eight years ago, but felt Italy striker Rossi was more deserving of the prize, having started the three games before the semi-finals during the cup run.
Current Fiorentina forward Rossi, who had only recently turned 19 at the time, did not make the bench in Cardiff with Sir Alex Ferguson instead preferring to give January recruits Patrice Evra and Vidic an important first taste of glory with the club.
Following the successes in the competition in 2009 and 2010, the skipper still has a chance of adding another League Cup gong to his collection even though he is now suspended for the semi-final second leg with Sunderland on Wednesday.
"It was a great match against Wigan," he recalled in an exclusive interview with MUTV and ManUtd.com which took place before Sunday's game at Chelsea. "We played really well. I came on for the last few minutes and it was a good experience. We scored four goals and could have scored five or six. We played really good football and it was important to win that trophy because we hadn't won a trophy for nearly two years. After that, we started to win things again.
"I only played for a few minutes in the final and got the medal and, afterwards, even though it was a nice feeling and I felt part of the team, I gave my medal to Giuseppe Rossi because I felt it would be better to give it to someone who had played more minutes than me in the competition. He deserved it."