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United were knocked out of Europe as Real Madrid claimed a 2-1 win at Old Trafford at the start of this month.
However, Real's win was marred by the controversial red card to Nani - which came when United were leading 1-0, but they could not hang on as Real claimed victory.
Van Persie still thinks that the sending off was crucial and, speaking whilst on international duty with Holland, he told AD.nl: "That red card was hugely unjustified.
"It was not even a yellow card or a free-kick. Nani couldn't do anything about it, he hardly touched Arbeloa.
"For an hour everything was looking good, the tactics seems to be right. We really had the feeling that we were going to make the second goal and then it became very difficult for Real Madrid. But then it was the referee pulled the red card. "
Van Persie was critical of UEFA and their decision to appoint Cuneyt Cakir as referee.
"The worst thing is that the UEFA supports him. That's cowardly, because I really don't understand it," he said.
"Why don't they say honestly: 'He hasn't seen it?'
"I didn't understand beforehand that this man would be the referee. Such an unknown referee who hasn't had any big games for months.
"The guys from Madrid said afterwards that it was not a red card. It's too bad, because bigger matches than Manchester United-Real Madrid won't come.
"So now it's all about the title in the Premier League."