The Red Devils are into the semi-final after beating Stoke City 2-0 on Wednesday night and the French left-back, who scored the second goal, is looking to clinch a first league cup since 2009/10.
"I think it is very important to win a trophy. I remember that the Capital One was my first trophy when I joined Manchester United," the acting captain told Sky Sports.
"Everyone is focused to win because it is an early trophy and it can build a lot of confidence for the team. That's why we really want to win this trophy."
Evra added: "We go through to the semi-final now and I think everyone did very well, even the players who don't play very often.
"The win was the most important thing tonight. The spirit tonight was the right spirit, the Man United spirit, the winning mentality. Now we are focused on the next game on Saturday (against West Ham)."
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