Accies secured their place in the Scottish Premiership courtesy of a penalty shootout victory over Hibernian at Easter Road in their playoff final second leg this afternoon.
The visitors had to overcome a two-goal deficit from the first leg to force penalties, but Neil insists that he always had a "feeling" his side would emerge victorious.
"I am delighted, for the players and the fans. A lot of people wrote us off but I didn't feel it was a 2-0 game and we played well first half. I told them to believe in themselves and to believe they could do it and once we got the first goal it changed a lot," Neil told reporters.
"My team talk was just telling them to believe and telling them to create chances - and take them. I don't think the Hibs managers and players through it was job done - but people in general did. I always believed we would win. I just had a feeling. I don't know what it was.
"I was actually going to play myself but I had a feeling and I took myself out of the team again. I changed it about and to a man we were unbelievable. The effort we put in was incredible. I saw Kevin Phillips saying the best way to go up is through the play-offs and now that we've done it, I know what he meant. It's incredible."
Hamilton return to the top flight after a three-year absence.