The left-back also admitted he thinks he and his side haven't been anywhere near their best, despite helping them breezing past Senegal in the first round of the knockout stages.
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England's 2022 World Cup campaign has been impressive so far, with Gareth Southgate's side finishing top of their group and winning all but one game in Qatar.
Their only draw came in the 0-0 against the USA in their second match, but they still finished two points ahead of the Stars and Stripes.
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But for Shaw - who plays his club football with Manchester United - he thinks England side can do much more moving forward, particularly against France on Saturday in the quarter-finals.
"The results we've had, the goals we've scored, and I think even at times we haven't been anywhere near our best," Shaw told talkSPORT.
"But we're still reaching high numbers in the goals scored, the chances we're creating. So I think that's the positive thing that there's obviously more from us still that we can do and reach another level.
"But at the moment the level's good, but like I said we need to step up another level on Saturday night."
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The game against France will pose as a real test for the Three Lions, and Shaw is set to be tasked with snuffing out the threat of Barcelona man Ousmane Dembele.
But Shaw - who is likely to start on Saturday - told talkSPORT he thinks England will be at their best if they're able to make the most of their attacking threat against Les Bleus.
He continued: "We need to impose ourselves I think, especially after the way we've been over the last few games. I think the attacking approach when we do do it at times is world class and can break down any team.
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"So I think we need to be on the front foot, we don't want to go into the game passive and sit back and go for that.
"We need to be on the front foot, more attacking because with the talent we've got, we need to be like that, we need to be on the front foot."