Goals from Ellen White and Rachel Yankey set up a game against France in Leverkusen on Saturday.
"We had a game plan, the girls implemented it, we've topped the group and it can only increase our confidence," Powell told BBC Sport.
"We were very, very good and I'm so proud of how well the girls played."
England needed to avoid defeat against Japan to be sure of reaching the last eight.
They got off to the perfect start when White's lob put them ahead after 15 minutes, with Yankey's clever finish in the second half wrapping up the points.
"The ambition was to get out of the group," added Powell. "We're still in the competition, we're not going home and that is brilliant for England.
"We made some changes to the team and they worked out, but we always knew it was going to be a squad game. Our opponents from now on doesn't matter.
"Sophie Bradley was enormous, Jess Clarke did a job in the first half, we changed a few things and the girls did really well."
White, who impressed throughout the game and could have had a second goal when her acrobatic volley was tipped over, admitted scoring was a dream come true.
"It's indescribable, the feeling of scoring in a World Cup," said White. "It's the pinnacle of your career to play in this tournament.
"I don't know what came over me for that," she said of her near-miss. "I was pretty unlucky but I'm pleased I got on the scoresheet to help the team.
"We stuck together as a team and implemented the game plan, which we try and do every game but this one really worked.
"We always had somebody kind of filling in, always there pressing the ball and worked really hard for 90 minutes and got the end product.
"I think we deserved to win the game in the end. I'm so pleased we got the three points and we topped the group.
"We know that if you want to be the best you have to beat the best, so we're happy to take anyone on now we're in the quarters.
"They are a great team, Japan, and they put up a real fight and it was a hard game so it was a great win for us and a good team performance."
England women's coach Hope Powell praised her players after they beat Japan 2-0 to reach the quarter-finals of the World Cup.