Chris Ashton's late try edged England in front for the first time in the match in the 78th minute to seal a late triumph at Eden Park which secured a quarter-final clash with France.
Moody told ITV1: "Full credit to Scotland. It was an incredibly tough day. They played a tremendous game. We knew they would and we didn't make it easy for ourselves by any stretch of the imagination with the penalty count.
"But we can only win the games in front of us and we've done that today.
"We've come out on the right side of the result but it was a tough game."
He added: "We knew Scotland would come out with all their fire and they did and in the second half we counteracted that.
"The front-row boys did a fantastic job at the scrums. We started getting on top of them in the second half, we got more of a platform and Ashy got over in the corner as he always does.
"It's another win - that's all we're here for and that's all that matters."
But, while England scraped through, Scotland were left contemplating elimination in the group stage of the World Cup for the first time ever.
Scotland need Georgia to beat Argentina in Palmerston North tomorrow - and deny the Pumas any bonus points - if they are to snatch a place in the last eight, but coach Andy Robinson was proud of his troops.
He told ITV1: "I've got to give every credit to the side. They've given everything.
"We're hugely disappointed to lose the game, as we were last week [13-12 defeat to Argentina].
"There's a great spirit among the boys. The way they have carried themselves throughout the World Cup, the friends they've made - I think they've been an outstanding group of people and I've been delighted to be their head coach.
"We're going to be supporting Georgia tomorrow. We hope they can do a job for us. I think the big thing is that sport is won and lost by inches. In both cases where it's come to winning games, we've lost out.
"But you can't fault England. They've held it together under pressure and seen themselves through."
Scotland had been inspired by a man-of-the-match performance from Dan Parks. They led 9-3 at half-time and 12-9 with three minutes remaining when Ashton dived over in the corner.
Johnson was pleased with the way his side upped their game after the interval.
"In the first half we didn't really have any ball in their half. When we did we got penalties 30, 40 yards out - they were tricky kicks," the England manager told ITV1.
"Six points down in a game like this, it's tough.
"The guys handled it really well. We got on top in the second half.
"We didn't always get rewards but we kept hammering away and I think the team that scored the try was going to get ahead. We took that pretty well.
"We just had to get the initiative. We let them get the initiative, the momentum - they probably looked more urgent.
"They were in the game [in the first half] and we weren't."
Ashton was pleased to have made a telling contribution but admitted there was plenty of room for improvement.
"It came together in the end but we need to get it earlier," he told ITV1. "In the next round we have to be better than that."
Asked if he had ever scored a more important try, he replied: "I hope so next week, but so far no. Three points down with five minutes to go, we cut it fine but we managed to get there.
"It's harsh taking Scotland out. We knew they were going to [put us under pressure]. In the Six Nations they made it hard work for us and they did the same today.
"I thought they did a great job."
Ashton was at a loss to explain why England were taking so long to get going.
"I'm just stood on the wing waiting for the ball - you're asking the wrong man," he said.
Scotland captain Alastair Kellock agreed with Robinson that there had been a fine line between victory and defeat.
"The difference was Argentina and England maybe had one or two chances and were very clinical when they had those chances," he said.
"We created opportunities to score tries but we didn't take them.
"We should have kept building the pressure. We were making them do things they didn't want to do. But when they got the chance they took it very well.
"There's never a doubt about our commitment. To a man we left ourselves out there."
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