Nani was withdrawn at half-time of Sunday's defeat and, although United were privately furious at Carragher's challenge, which they felt merited a red rather than a yellow card, they have not commented on the incident because of a media black-out imposed by Sir Alex Ferguson.
United's manager refused to speak to any media outlets after the game, including the club's own television station, and instructed his coaching staff and players to remain silent.
Sources close to Nani said the winger believes the club should have shown support for him publicly. United's chief executive, David Gill, was sufficiently incensed by Carragher's tackle to voice his complaints to the referees' chief, Mike Riley, at half-time in the directors' box.
Carragher tried to apologise to Nani after the game but it is understood the Portuguese was unwilling to engage with the defender, who was denied access by United's players to their dressing room. He then waited outside with the intention of saying sorry but Nani is understood to have walked by.
Nani does not expect his injury to sideline him for long. "I would like to thank supporters for their good wishes and I hope to be back really soon," he said.
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