The Black Cats won a tense penalty shootout 2-1 after both sides scored at the end of added time to make it 2-1 on the night.
"The feelings are for them," the Uruguayan told Sky Sports News, referring to the visiting fans. "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 now face Manchester City in the League Cup final.