It been a frustrating 94 minutes for the Black Cats who had dominated possession but struggled down a resilient Gillingham side, before Broadhead combined with Elliot Embleton to produce a crucial winner with seconds left on the cross.
Neil admitted that his side could have done more to test the opposition goalkeeper through the game but insisted the late goal was a fair reflection of their efforts.
“I don't think it's any more than we deserved really,” Neil said.
“I thought the performance was very good and I know it took us to the 95th minute to score the goal, but you couldn't be critical of the amount of times we got the ball into the final third.
“Okay, maybe the final ball at times, the final run, the final pass, but with 25 shots at goal.... we only had five on target which we certainly need to improve but at this stage of the season it's about getting the job done.
“We were really dominant, pinned them back in. I'm not bothered who you are, it's hard to beat a team like that who put ten behind the ball.
“I've watched Ipswich Town against them and they won 1-0 with the help of a deflection, I've Sheffield Wednesday against them draw 0-0. They're hard to break down, and I've said all week how hard that was going to be. We produced the moment of quality when we needed it.
“It's taken about ten years off my life, but we got there.
“I don't get ahead of myself, we've done what's required today and I'm really pleased,” he added.
“It's just going to be that snowball effect isn't it, every game becomes bigger and bigger.
“I think we could have won by more today, but we got the job done.
“There's a long, long way to go and we've got a lot of big games coming up. As you can imagine, I don't get too high and I don't get too low.
“We deserved to win the game, and I’m really pleased with that.”
Neil also added his satisfaction with another clean sheet, which he says will be the bedrock of the push for promotion.
“That was something that needed fixing,” he said.
"I spoke about it quite a lot when I first came in because the stats were there, it wasn’t an opinion, it was a fact. I think what we’ve got now is a real platform to go on and win games, and if we can continue that, it’ll bode well for us going forward.
"There’s only two facets of the game, isn’t there? What you do when you’ve got the ball, and what you do when you don’t have it. What you can’t be is easy to play against, and let teams score against you, and then not be able to create going the other way.
"At the moment, it’s hard for us to break teams down because they’re playing with banks of ten behind the ball. But equally, we’re not easy to play against and I don’t think teams will look forward to playing against us.”