United moved to the top with a comfortable 2-1 victory over Arsenal at Old Trafford but Ferguson felt they should have had much more to show for their near total dominance of the match.
Robin van Persie struck against his old club inside three minutes but despite a superiority in almost every facet of the game, United never threatened to repeat last season's 8-2 humbling of the Gunners.
United missed a number of chances including a penalty - Wayne Rooney dragging wide from the spot - but Patrice Evra made the scoreline more comfortable with a 67th-minute header.
Yet even after Arsenal had Jack Wilshere sent off, United might still have faced a nervy finish had Santi Cazorla's injury-time consolation come a couple of minutes earlier.
Ferguson said: "I'm disappointed with our inability to hammer home an advantage.
"I spoke about goal difference to them at the start of the season.
"We lost (the title) on goal difference last season and I don't want to see that again. We had an opportunity to add to our tally."
The game lacked the intensity of some of the memorable clashes the clubs have fought out over the past decade, mainly because Arsenal were outshone.
Coming after last week's ferocious battle with Chelsea, it was quite a flat encounter for United and Ferguson grew concerned as the game unfolded.
He told MUTV: "It looked as though it was going to be self-destruction. It only takes a second to lose a goal.
"They had some possession without threatening us but thank God we got the second one because with them scoring right on time, it would have been an embarrassment."
Penalties are also a worry for the Scot, with United having now missed four of their six spot-kicks this season.
Ferguson said: "I know, I think I will take it myself next week - if we get one."
Defender Rio Ferdinand responded on behalf of the team by saying Ferguson's feelings over a lack of killer instinct were shared by all the players.
Slip-ups by Chelsea and Manchester City elsewhere may have left United as outright leaders, but Ferdinand felt the mood in the camp was not that usually associated with victory.
The 33-year-old said: "We should have finished that game off ages ago. That is the most disappointing thing.
"If you had been in our changing room you'd have thought we lost the game, the way the mood was.
"At the end of the day it is three points. I thought it was the best shape we have had for a while, this season, and we defended as a team.
"That showed in the amount of chances we created but we should have maybe had the game won by five, six or seven but it wasn't to be."
Arsenal's defeat was their second in three league games and left them nine points off the top after their worst start to a season in manager Arsene Wenger's 16 years in charge.
Their agonies were compounded by the dismissal of Wilshere, who had been in just his second game back after a 14-month injury absence, for a second yellow card.
Wilshere had perhaps been lucky to escape a second booking earlier but his departure was inevitable after a bad challenge on Evra on 69 minutes.
United's Tom Cleverley had found himself in a similar situation after some mistimed tackles, but Ferguson withdrew him for his protection.
On why he did not take a similar decision, Wenger said: "We had to go forward and attack, they were more in a position where they could defend.
"We did not have a lot of central midfielders who are offensive on the bench."
Wenger was urged to "sort it out" by angry Arsenal fans, who also vented some of their fury at chief executive Ivan Gazidis.
Wenger felt the loss of the early goal did much damage.
He said: "They had better chances than we did but in a big game like that you have not to put yourself on the back foot by going 1-0 down.
"But if we had stayed 1-0 and 11 v 11 maybe we would have had the chance to come back."