Gus Poyet dedicates dramatic win to Sunderland's 9,000 travelling fans
The Black Cats won a penalty shoot-out 2-1 after both sides scored at the end of extra-time as the match ended 2-1 to United.
"The feelings are for them," Poyet told Sky Sports 1, pointing to the visiting fans at Old Trafford
"A difficult season, nothing to enjoy, look at them, they deserve that. Let's see if we can go one more and win it."
Sunderland will be rank underdogs in the final against Manchester City, but, having knocked out Chelsea and now United, that is a status Poyet is happy with.
And asked if his side could win, the Uruguayan added: "No doubt, for sure."
Sunderland goalkeeper Vito Mannone, who saved the decisive penalty from Rafael, said: "Unbelievable, just unbelievable. I just want to celebrate with my team-mates.
"We deserved to get to the final."