The French full-back, who skippered the side on Wednesday night, netted a rare goal in a 2-0 victory over Stoke City - and an even rarer one with his right foot.
His strike built on Ashley Young's spectacular opener and helped United to set up a two-legged tie with Sunderland in the last four.
Evra hopes United's quest for major silverware will carry them all the way to Wembley, with any trophy considered to be vital during the early days of a new era for the club under David Moyes' tutelage.
He told Sky Sports: "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.
"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."
On a hard-fought victory over Stoke, which was halted for 10 minutes in the first half as a heavy hail storm hit the Britannia Stadium, he added: "The conditions were very difficult but I think we have to give credit to all of the lads because it was not easy. To win at Stoke 2-0, to keep the clean sheet again, we are very pleased with the victory.
"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."
Young also found the conditions tricky at times, but was delighted to offer a timely reminder to Moyes of what he can offer amid talk of a possible January exit.
He said: "The conditions were crazy. I think the boys wanted to stay on instead of coming in and getting dry, but I've got to say that we did magnificent. It was a great team performance. We showed great spirit and character out there.
"Of course I want to play more. I have been on the bench and coming off, so I want to be in the team. Every player wants to play in the starting line-up and I'm no different to that."