Sunderland won 2-1 thanks to Brighton-bound Tommy Watson's injury-time winner.
Afterwards, Bellingham said: "It means everything to everyone here for all the staff, for everyone involved. It’s all the club have been aiming to achieve for eight years.
"Every single player has spoken about it when they have come here to get this club back to the Premier League and so many have failed but I take a lot of pride in saying that I am one of the players who has helped this great club get back to where it belongs.
"I always believed, you have to believe, when you have supporters like this and a group of lads like this, you have to believe."
People doubted us
On their doubters after losing their final five games of the regular season, Bellingham also said: "I know people doubted us, it was understandable, we lost a few games, people talk about momentum, but I think we did enough and showed enough in the season for people to give us some credit going into the play-offs.
"People say we are inexperienced but you get experience by failing and we have failed together so many times and in the end we've come good.
"Every single player has made a name for themselves here. Really proud."