City, who had not won at the ground since 1974, completed their first league double since 1970 with a deserved win.
Darius Vassell and new boy Benjani Mwaruwari scored first-half goals for City and United's only reply was in injury-time from Michael Carrick.
There had been fears in the weeks leading up to this emotional match, which marked the 50th anniversary of the Munich air disaster, that City's fans would disrupt the silence in memory of the 23 players, journalists and officials who died on February 6, 1958.
But the City fans respectfully observed the period of silence and emerged from the match with their reputation in tact.
"I am extremely proud of our team. If you go to Old Trafford and win you deserve it," Eriksson said.
"But everyone who belongs to City, players, officials, must be proud of what our fans did here. Their behaviour was fantastic and I am extremely honoured to be the club's manager.
"I have never been involved in a ceremony like that before, it was a very nice experience to be able to pay our respects.
"The two teams together, and all the fans, absolutely silent for one minute. It was beautiful.
"There has been a little concern for everyone at the club, maybe even the fans, that something may go wrong. But they were not just good, they were perfect."
Eriksson continued: "Everyone was wonderful. The goalkeeper was good, all the defence and midfield were good, Benjani up front was excellent, I am really proud of the players and also our fans.
"You can't come to Old Trafford and give them space because they can over run you.
"We were defending one goal, then Benjani got us a second when we were under pressure and that gave us something to really hang onto.
"Benjani did very well, he is quick and keeps the ball, he also works very well defensively.
"I am also very proud of our fans, they were perfect before the game and fantastic right through the 90 minutes.
"I understand the history, and the last time City won here or did the double over United. It was far too long and we have now corrected that.
"It was time to out that right, and we have done it and given our fans something special."
Sir Alex Ferguson did not conduct any media interviews after the game.
The United boss headed straight to the airport after the final whistle to catch a plane to South Africa, where he will be promoting the club's pre-season tour.