The veteran Scot was infamous for his protestations towards referees and his Rs counterpart feels that his "aura" may have affected decision-making.
"A lot of officials would be in awe of him and afraid to upset him. There was such an aura about him because he is a winner," Redknapp told BBC Radio 5 Live's 'Sportsweek.' "I never had any doubts about that. If there was a bit of time to be added they would make sure they got it right, because they did not want to upset him. Especially young referees, and even one or two of the older ones, were a little bit afraid to upset him."
Redknapp also admitted that he had not expected his United counterpart to retire just yet.
"I think we all knew it would come suddenly. I thought he would go on for a couple of years yet," Redknapp said. "He has won the Premier League and maybe feels it is a good time to go out and enjoy his life. Maybe he wants a bit more time to do stuff away from football.
"He has put great teams together. He has known the right time to let people go and never been afraid to make the big decisions. Whether it was Roy Keane, David Beckham or Jaap Stam, all the great players have come and gone. He knows the game inside-out."
David Moyes has been appointed to succeed Ferguson, an appointment the Rs manager welcomes.
"It is great for British coaches that Manchester United have picked someone who has come up through the lower divisions," Redknapp said. "It is good they have given the opportunity to David Moyes; I think he will be fantastic.
"It is a tough job. Moyes built a great team at Everton, and I'm sure he will do a great job at Manchester United."