An injury-time goal from Tom Watson earned Sunderland a 2-1 win against Sheffield United on Saturday and promotion at Wembley.
Neil told Sky Sports: "This whole city has come together in the last two weeks.
"That's what Sunderland football club is - it resonates with all the people and when it comes together it's a powerful thing.
"For it to end with a last minute winner in the semi-final and then today it's not even what dreams are made of because you wouldn't dream of something like that.
"It's been a massive team effort and that's our biggest strength - the team.
"I don't know when it will sink in but we're going to have a heck of a party because it's been a season of ups and downs and this game sums it up, going 1-0 down, keep fighting and we got there in the end."
Patterson thrilled with victory
Meanwhile, goalkeeper and man-of-the-match Anthony Patterson also said: "Honestly it's in incredible, I don't think I can put it into words, so proud of the boys, they stuck in right until the end and we got our rewards. I'm so happy."
On being with Sunderland since they were in League One, Patterson added, "I've not even thought about it, it's not even sunk in what's happening but I'm gonna enjoy every moment now."