Houghton and fellow defender Lucy Bronze scored the all-important goals as England came from behind to beat the 1995 champions and record their first win in a Women’s World Cup knockout game.
Substitute Jill Scott played a part in both England goals but Mark Samson’s side were also indebted to goalkeeper Karen Bardsley, who produced a string of fine saves as England progressed to the quarter-finals.
“Karen pulled off two fantastic saves in the first half to keep us in the game when we were in that defensive mindset,” White told Sky Sports.
“But it was two fantastic goals, first from the skipper Steph, who stepped up and did it again at another big tournament (after finishing as Team GB’s top goalscorer at the London 2012). She scored yet another vital goal and the other one was a great strike from Lucy.
“You need players to step up and I think Jill Scott did brilliantly and we had more of an attacking intent when she came on. She’s not a right winger but she came on and she filled that position and done what was needed for the team. But that header from Steph gave us the confidence and that’s when I think we started to see the real England.”
White added: “We still need to learn how to control the game like the best teams. Germany and America can control the game from the off and do it for 90 minutes.
“Are we there yet? No we’re not. So we must play to our strengths and when we play with belief and positivity, we just look like a different team.”