The Reds hosted Sir Alex Ferguson’s side in March and Anfield saw Dirk Kuyt net a hat-trick as Luis Suarez starred in the victory.
However, Carragher was booked just before half-time for a high challenge, catching Nani in the shin which left a deep gash and prompted the medical team to stretcher him off the field.
Nani, who returned to action two weeks after the contact for United’s Champions League game against Marseille, criticised the 33-year-old for his dangerous tackle.
The experienced defender admits he was relieved that his challenge had no hugely serious consequences for Nani.
"It was a terrible tackle," Carragher told Goals on Sunday.
"I apologised to the lad after the game. I think he was training again after a week, fortunately.
"He's been one of the best players this year - not just at Man Utd but in the league.
"I'd just gone to full-back and he'd just switched sides. I'm not stupid - I know Fergie was thinking 'Let's get at him'.
"So I thought I'd try and get as tight as I could. He slightly mis-controlled the ball and I thought I could get it.
"We beat Man Utd, great win - but it took the shine off it a bit later on when I watched it.
"I spoke to Michael Owen a few days later to find out how the lad was doing and I was pleased he was okay."