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City fired a rare blank at the Etihad Stadium on Sunday with Haaland enduring a frustrating afternoon, touching the ball just 23 times, as they lost ground in the Premier League title race.
Keane was left unimpressed by the 23-year-old's performance and said: "In front of goal he's the best in the world, but his general play for such a player - it is so poor. Not just today. He has to improve that.
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"He's almost like a League Two player - that's the way I look at him. His general play has to improve. It will do over the next few years. [He's a] brilliant striker but he has to improve his overall game."
However, speaking ahead of City's fixture against Aston Villa on Wednesday night, Guardiola defended Haaland and claimed it wasn't the striker's fault that his team didn't score.
"I do not agree with him, absolutely not. He's a manager for the second or third league? I don't think so," said Guardiola.
"He's the best striker in the world and he helped us win what we won last season. The reason why we didn't create many chances [vs Arsenal] was not Erling, it's that we need more presence in the final third with more people.
"We played an exceptional game, I reviewed the game against Arsenal, but we missed more people in the final third maybe for the quality and skills that we have. Erling is exceptional.
"I'm surprised this came from a former player. From journalists, I can understand, never been on the pitch but former players is always a surprise. It's like the referees when they retire they criticise the referees.
"How difficult is that business for the players? It always surprises me. Their memory disappears quickly. The problems the players have, they had. They missed a thousand, million times and they were hurt when they were criticised by the former players.
"But today is what it is. We have to accept it and move forward. I don't know what's going to happen in the future but I'm not going to criticise my colleagues when I retire. 'Should be this, should be that, could do that' - I could do it now and I don't do it. But everyone has to live for something.
"Players have to accept it, it's the job. If you don't want to accept it you have to do another job. When you're this public figure you have to accept it."
Haaland has scored just once in six attempts against the top five sides this season although Guardiola insists it's down to the team.
"Sometimes he misses, sometimes lack of supply, sometimes instructions from the managers, sometimes the opponent is really good," said Guardiola. "In football there is not just one reason, there are many. Football is a team sport, it's not individual like golf or tennis."
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