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After an imperious run of form at club level saw him return to the England starting XI, Stones made a costly error in the second half when his heavy touch allowed Brighton's Jakub Moder to level matters at Wembley.
The former Everton man would then atone for his mistake fives minutes from time as he headed down a corner for centre-back partner Harry Maguire to smash home the winner and make it three wins from the opening three World Cup qualifiers for Gareth Southgate's side.
The blip from Stones, a rarity in recent times, was highlighted but former Arsenal and England striker Wright pinned some of the blame on Nick Pope - who has struggled when it comes to his distribution.
"What we saw there, I'm quite pleased with Pope getting his chances but what we saw with the way he passed that ball to John Stones, obviously John Stones is going to get the blame for it, there wasn't a lot going on, for me it wasn't a pass that he should have made," Wright said on ITV.
"He passed it in a way that he had to deal with it. It was a poor decision for the goalkeeper to give him the ball in the first place. So I feel for him because he has had a great season and now people are going to judge him following that."
But fellow pundit Keane wasn't having it. With Stones regularly looking comfortable on the ball for Manchester City, the Irishman accused him of getting "bored" and losing concentration.
"There was obviously parts of the game they were disappointed with. John Stones, some defenders do get bored and I think he may have that in his make up," Keane argued.
"I'm going to disagree with Wrighty, I don't think it was the keeper's fault tonight.
"Okay, he didn't give him a great ball but Stones is used to playing out from the back with Man City.
"Lack of concentration, Stones got bored. That's why they gave away the goal. I wouldn't blame the goalkeeper for that."
Maguire, scorer of the emphatic winner, came to the defence of his friend and defensive partner - praising him for the way he responded to the mistake.
"Defenders can always make mistakes and sometimes we are at fault for goals and John has obviously had a little blip tonight," the Manchester United captain said post-match.
"I said to him 'keep going and we'll get the win' and he made up for it with a great header at the back post for my goal.
"John has been brilliant this year and I'm sure he'll not make a mistake like that again. It was a big performance from him to react like and come back with the assist."
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