Iran, managed by Queiroz, scored through a Moroccan own goal in the 95th minute, the last minute of stoppage time, of its opening game in St Petersburg to secure only the second World Cup victory in its history.
The former Manchester United assistant coach paid tribute to Sir Alex, who is recovering from surgery after a brain haemorrhage in May.
'I have not been able to see him since he was taken ill, but as soon as he is strong enough, and I get the chance, I will go to see him and give him a hug. He is a great man, and a great friend.'
Queiroz was assistant to Ferguson twice, and has been manager of Iran since 2011, Daily Mail wrote.
Their victory on Friday, coupled with Portugal's dramatic draw with Spain, means Iran are top of Group B, and he said, 'I am proud of these players.'