Lee Gregory looked to have sent the tie to extra-time when he converted Marvin Johnson’s low cross with fifteen minutes to play, but Sunderland found another gear to score when Jack Clarke squared for Patrick Roberts.
There were still nine nervy minutes to see out at that stage but the Black Cats did it without giving up any significant chances.
Neil said he felt it was a deserved result both on the night and over the two legs. He also spoke of his relief that his decision not to make changes after the goal paid off.
“When that goal goes in, there's so much emotion that it's just hard to describe,” Neil explained.
“Unfortunately I'm quite aggressive when I show all that! I don't try to be!
“If I'm honest I'm just so pleased for the players, because they do get written off. People talked about coming here, Sheffield Wednesday being favourites. So they can put that in their pipe.
“I thought it was no more than we deserved.
“We've switched off once and been punished for it. We've defended really well up until then, we didn't try to be defensive with our selection.
“I didn't think we deserved to trail, and I don’t think anyone I just said to the lads, ‘it’s a moment, it’s done, it’s gone’. And I thought we responded really, really well.
“It's probably the first time I've not made early changes and that's because I had so much faith in those players.
“I felt if I changed it, I might dilute what we're doing. I had to stick to my guns but I believed in what that team were doing for me. They delivered for me again.
“But for us, it's only got us to an opportunity now. We've celebrated, but it won't be long for none.”
Neil said his side have shown again the resilience he has looked to instil since taking charge.
“The one thing you want as a coach is your team to represent you,”
“I would regard myself as determined, focused and knowing what I want, doing everything I can to get it.
“I think this team completely represents me.
“And the thing is, they then have qualities that unfortunately for me I never, ever had as a player.
“So if I can take that work-ethic, that determination, and put their quality next to it, it's a good recipe.
“We’ve got another job to do, but it was only three months ago that I was sitting in the house, hoping a big club might take a chance on me. In football you’re quickly forgotten, and that’s not lost on me.
“I feel really privileged to have been given an opportunity and I really want to repay that by delivering success.
“I’m extremely proud to be here, leading this group of players.
“We’ve now given ourselves a chance to get out of the league.”