"We won the game and three wins is very good and I hope we can go on like this," said Eriksson, whose team are two points ahead of Chelsea.
"It's good to have such a good start when you have so many new players and the confidence goes higher and higher." Ferguson praised his team for creating scoring chances but blamed his forwards for wasting them.
"We had an awful lot of chances. We played some fantastic football at times but it wasn't our day," he said.
"We were just wasteful. I don't think you can even say we were unlucky because we had so many opportunities to win it ourselves. It was our own fault."
United controlled the first 30 minutes and could have been two goals ahead before Geovanni scored for City.
When Carlos Tevez and Paul Scholes opened up the City defence in the fourth minute, Nani got clear but his shot was blocked at the foot of the near post by goalkeeper Kasper Schmeichel, the son of United great Peter Schmeichel.
The City goalkeeper also saved again from Nani, and Patrice Evra was tackled as he was about to shoot with only Schmeichel to beat.
"It's fantastic. But we were lucky," Eriksson said. "If the game were based on possession of the ball or shots on target we would have lost. But it's goals that count."
At Anfield, Fernando Torres collected a slick through ball from Steven Gerrard and burst past Chelsea defender Tal Ben Haim before sliding it inside the far post.
The Blues were gifted a 62nd-minute equaliser by referee Rob Styles, however.
Chelsea forward Florent Malouda jumped into Steve Finnan as a cross came over from the right and Styles ruled that the Liverpool defender was guilty of the foul, leaving Frank Lampard to score from the penalty spot.
"I think it was a mistake. It's unbelievable. How can you take this decision?", said Rafael Benitez, the Liverpool manager.
"The game was under control but this kind of decision is something you cannot respect."
Jose Mourinho, the Chelsea manager, wasn't sure his team was lucky to get the penalty.
"I don't know. So many times you are unfortunate, especially in this stadium, with referee decisions," he said.
"It was a tough game for referees."