The 2010 World Cup winners were given a fright when they edged through to the Round of 16 in second place, after leading the group at kick-off.
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Japan came from behind to beat Luis Enrique's side 2-1 to take top spot in Group E, meaning they will face Croatia on Monday, while the Spanish take on Morocco.
Spain were dominant in the early stages but were pegged back by quickfire goals early in the second half from Ritsu Doan and Ao Tanaka.
Simon was at fault for Doan's equaliser when he appeared to misjudge the flight of the ball after the Japan forward unleashed a 20-yard effort.
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The Athletic Bilbao goalkeeper then palmed the ball into his own net which became the catalyst for Spain's subsequent collapse.
Neville was critical of Simon's role in Japan's leveller during his post-match analysis for ITV and called into question his starting place for the remainder of the World Cup.
"The big decision for the game is whether [Spain] stick with the goalkeeper," said Neville.
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"[Simon] is the one part of their game that looks like a real weak point and I have to say it starts off badly. We know they like to play out the back, we know they like to take chances and we want them to continue to do that, we're not trying to change that.
"He's got to save that [Doan's goal]. They've got Raya on the bench and they've got Sanchez."
Neville then insisted Manchester United goalkeeper De Gea would have comfortably dealt with Doan's effort.
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He added: "They've got De Gea still at home. I know he's not been brilliant these last few years, but I can't think he'd let that one in! That's a real bad one. In a knockout game that's fatal for you."
De Gea, was axed from Luis Enrique's 26-man World Cup squad despite having amassed 45 caps for Spain.
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