The Portuguese superstar scored the crucial goal to secure a 2-1 success on the night and a 3-2 aggregate triumph to send the Spanish giants through to the quarter-finals.
Nani's red card in the 56th minute turned the match, with United leading at that point after Sergio Ramos' own goal, only for Luka Modric and Ronaldo to dump the Red Devils out.
Ronaldo, who spent six years with United from 2003 to 2009 before joining Real in an £80million deal, was afforded a warm welcome back to his former stamping ground by the home supporters.
And he told Sky Sports: "It was unbelievable, it was an emotional moment for me. I don't have the words to explain what I feel.
"What the supporters do for me made me feel shy because, in my opinion, in both games I didn't play like I play all the time, to a good level. But I helped my team by scoring one goal at home and one away.
"I am happy inside because Madrid got through, but on the other hand I feel a little bit sad because of Manchester United. But it is part of football, and I am wearing the white collar."
Ronaldo has been linked with a possible return to Old Trafford in the future, and while he would not rule out a shock comeback, he preferred to focus on the present with Real.
"In the future, you never know," he said. "The supporters and the club, it is massive. You never know, but I am very happy at Real Madrid and I want to be there.
"We have had an unbelievable week, winning both games against Barcelona and then beating Manchester United. We are in good shape and we want to carry on like that because we want to win this competition."