The Northern Ireland international was among the goal scorers as the Blues were subdued at the Stadium of Light before a defeaning home crowd.
Speaking of the achievement, Hume reflected on a season in which the club worked their socks off to overcome outside doubts after their promotion to the English top-flight.
“I can't put it into words to be honest with you, we fully deserved that all season, worked our absolute socks off throughout the year," he told Premier League website.
"When we first came up, no-one gave us a shot but here we are in the Europa League, proved a lot of people wrong and there's nothing better.
"I've played here for four-and-a-half years, they (the fans) are absolutely amazing every time, I knew if we scored first we'd win, they've been behind us all the time and that's what happened."
Hume arrived at Sunderland from Northern Irish club Linfield in 2022, when the Black Cats were languishing in League One.
Just four years later, he scored one of the goals to send them on their way to Europa League football.
"It's been a whirlwind journey, I signed here in League One and if you told me four years ago that I'd be here in the Europa League, I wouldn't have believed you.
"It’s a credit to the owner, the staff, players… the club's brilliant, everyone we've signed and those that have left, fantastic people and this is what we deserve.
"You've always got to improve every summer and winter window, try to keep getting better, we just work hard every day and see where it takes us."