Sarina Wiegman's side beat Austria 1-0 thanks to a poked effort from Beth Mead in the opening game of the tournament at Old Trafford.
While England's win will have eased the players' minds, there were moments when they looked shaky, with Wiegman admitting they were 'sloppy' on the ball at times.
Ex-skipper White, who wore her country's armband for ten years between 2002 to 2012, joined talkSPORT's Weekend Breakfast to discuss the Lionesses' start to the Euros.
talkSPORT's Natalie Sawyer asked White whether the standard of performance really matters, given they won.
And the Arsenal legend insisted that while the Lionesses will have been happy to just start to tournament with a victory, their performance will raise some concerns.
"I think when you're hosts it just matters about getting the three points," she said.
"Getting the win under your belt. There was obviously a lot of expectation and nerves I'm sure from the players so yeah I think they would be happy.
"If we get to the latter stages, no one will remember this first game."
However, despite getting over the line on Wednesday, White went on to state that England do still need to up their game, especially against their next opponents, Norway, on Monday.
"We'll have to improve our performances, certainly," the former Lionesses star said.
"Without doubt it's the toughest test [the next game against Norway].
"Norway are the top team along with England and you'd expect the two to go through. But it's going to be an even test I think.
"There will only be a couple of chances for each team in the game, and England have to be better at taking them."
Listen to live coverage of England vs Norway on talkSPORT at 8pm on Monday with commentary from Sam Matterface and former Lionesses striker Lianne Sanderson