The 20-time English champions lifted the EFL Cup courtesy of a 2-0 victory over Newcastle United, with Casemiro opening the scoring for Erik ten Hag's side before Rashford's shot was deflected past Loris Karius by Sven Botman.
Rashford said that it was "a massive feeling" to lift the silverware, with Man United also chasing success in the Premier League, FA Cup and Europa League this season.
"It's massive for us to be involved in these types of games, something that we've missed as a club," Rashford told Sky Sports News after the match.
"The fact that we've come all this way and we've gone on and won is a massive feeling but hopefully it pushes us now to keep going.
"I'm happy right now so it doesn't matter! I'm buzzing with the result, the boys and the staff have put a lot of work in to get here and to go on and win it is just a massive feeling."
Rashford was also keen to pay tribute to Casemiro, with the experienced midfielder again putting in a strong performance for the Red Devils.
"He makes a huge difference, his leadership and experience in games is huge," added the Englishman.
"I've spoken to some of the other forwards and on the pitch they feel that sense of security behind them. It's massive for us and I'm buzzing for him today, his first trophy for the club and hopefully he can push us now to get even more."
Fernandes, meanwhile, told Sky Sports News: "It's been amazing [to win the Carabao Cup]. First trophy of the season, but we want more. We want more.
"This is not enough for this club, we want and we need more, because, for our standing, we need more. For me, it was about winning trophies. Finally we did it, but I want more. I want much more."
The Portugal international also said to MUTV: "It's always incredible to be a Red, it doesn't matter if you win or not, it's always incredible.
"You see the support they [fans] give us in difficult moments, and now it's time for them to have some joy also because they've been behind us through the worst and now they deserve this. They deserve to be in this position with us."
Man United will now switch their attention to the FA Cup, with the team preparing to host West Ham United in the fifth round of the competition on Wednesday night.