The hosts were impressive throughout a challenging afternoon for the Black Cats, who nevertheless took an imposing lead through Ross Stewart and Elliot Embleton.
A defensive error allowed Troy Parrott to reduce the deficit midway through the second half, before a Lynden Gooch penalty miss made for a tense finish.
Johnson said the 3,000-strong Red & White Army, who were present for a league game for the first time since the start of the COVID-19 pandemic, were a crucial factor.
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The Sunderland head coach also praised his young side for coming through a stern challenge.
"I honestly thought they saw us through, they really did," he said.
"They kept us honest when we needed to apply pressure, they cheered every clearance and dragged us up the pitch when we needed it.
"It was a tough game for us. We're not going to get easy ones, though of course we can make it easier for ourselves by taking our opportunities.
"There were times where we could have managed it better but it's one where we'll have to look back objectively.
"There was a lot to take in from that game and it's one that I'm probably having to go and watch three or four times.
"We've built that bit of character there.
"We've had a huge squad turnaround, we had young players making their debuts, earning about how to cope.
"And we've come through another one.
"We've made it hard for ourselves, there's no doubt about that," he added.
"There's a couple of positions where we short today for various reasons, and Luke O'Nien was a big loss.
"But we've created some really good chances, too. I thought Ross Stewart should have had another penalty early in the second half, Alex Pritchard has had a really good chance to seal it and then Goochy obviously has the penalty which sent me into an early heart-attack.
"That obviously buoyed them but it is what it is.
"We've got to look at it objectively, we've played a good side who can drain you because of the way they hold possession and create overloads. But apart from the one great save, where Burge has showed some really great footwork to palm it over the bar, we weren't troubled hugely and certainly not in the first half.
"It certainly got tense but the boys came through."
Johnson also hailed academy graduates Dan Neil and Elliot Embleton, who combined to superb effect for that second goal early in the second half.
"Most goals are scored within those three passes so credit to them, that winning it back and switching on in the frenzy of the game is one of the absolute fundamentals of what we do every day in training," he said.
"It was great from Dan and a great position Elliot took up to receive it as well.
"It was a nice tidy pass and an excellent finish, because the composure was top draw.”