Keane was speaking after France's Euro 2020 elimination at the hands of Switzerland.
"No doubt it would be frustrating," the ex United star said on ITV. "But this is all part of Paul's character that people love to see and it's great.
"But then I'd be looking at the goal they conceded in injury time when he was sloppy in midfield, that's the bit I'd be really critical.
"It seems harsh because he's done some brilliant stuff going forward today, there's no doubt in Paul's quality, it's just the other side, maybe his maturity.
"United have had these problems. Can he play in a two midfield? He probably can't, he hasn't got the discipline.
"Even today he leaves you frustrated, even with his brilliant quality going forward he lacks that discipline defensively.
"The top players do it week in and week out and Paul doesn't quite do it."
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