The Black Cats boss admitted his frustrations with two soft goals conceded, but felt his side were worthy of their win and feels the defensive problems are ones that can be fixed.
"I said to the players before the game that this is one of those game where if you lose it, people look at it and say that's an average to poor start," Neil said.
"Win it, and people will say that's a really good start.
Supercomputer predicts final Championship table - including surprise finishes for Sunderland, Middlesbrough, QPR, Sheffield United and co
Sunderland AFC transfer news: Cats take 'brilliant' ex-Manchester United and Burnley midfielder on trial
Championship transfer news: Interest in £22million man, setback for Arsenal loanee plus Norwich reports
Sunderland AFC transfer gossip: Cats in 'final stages' of deal for 18-y/o eight-cap international winger
Sheffield United suffer injury blow ahead of Sunderland game with 264 goal striker potentially sidelined
"That's state of the season we're in at the moment. It's four points for us on the board, our first win which is important, and we've scored three goals [away].
"The one thing I'm disappointed with is the two goals we've given away, but that's probably me being greedy. They're errors, easily fixable and so not something I worry about from a structural point of view."
Neil felt the much improved bravery his side showed in possession through the second half was crucial to turning the tide of the game.
"We weren't brave enough in the first half, we didn't use the ball well enough, turned it too quickly," he said.
"We didn't step up from the back to make sure we got the extra man in the middle. The lad Atkinson did that really well for them, we played as a flat three which we weren't meant to.
"Once we stepped in front of them in the second half, drove the space and forced them to commit, we had the extra midfield player in there.
"When that happened, we dominated and we were able to get Jack Clarke a lot of the ball, whereas in the first half he was feeding off scraps really. Having said that, I said to him after that he has to do his job when we're not on top.
"There's a lot to improve on for a lot of players but I thought the second half performance was really, really good."