Nathan Broadhead’s only goal set the Black Cats on course in what was ultimately a comfortable afternoon as Plymouth Argyle fell to a heavy defeat against MK Dons.
The Black Cats will now face Sheffield Wednesday in the semi finals, with MK Dons and Wycombe Wanderers to contest the other tie.
“I'm really pleased with what the players have done,” Neil said afterwards.
“I think that's one in fifteen that we've lost, and that one still bugs me by the way.
“We've cleared the first hurdle now, we're in the play-offs, and now there's work to do.
“It was a tough game, scrappy in parts.
“Our goal was excellent and I thought our transitions, we should have made better use of but it's understandable when you consider what's at stake, they are fighting for their lives as well.
“The simple fact is we got the job done, and really I thought we did it with comfort. I don't think Patto has had a save to make in the end.
“If you look at their home record, their goal average is -1. Away from home it's -29, so that shows that this was going to be a difficult game. They've beaten Oxford here, they've drawn with Ipswich and Bolton.
“They make it difficult for teams here so it is a good win for us.
“We'll rest up tomorrow and then we'll get started [preparing for Sheffield Wednesday].
"I'll enjoy the moment but I won't get carried away,” Neil added.
"It is what it is, now I need to prep and plan.
"That's my focus now, no time to celebrate.... I might have a beer with my dinner tonight, maybe."
Sunderland’s major concern from the game was that Broadhead left the field with an injury during the first half, casting doubt over his possible play-off involvement.
The Everton loanee was a doubt before the game but Neil says the issue is unrelated.
“It's a completely different area I believe,” Neil said.
“The worry we've got now is we've finished the game with no centre forward on the pitch, I brought Stewart off because I knew the scores elsewhere.
“He's literally [our only striker].. I don't need to say anything else do I?”