United's jaw-dropping win on Sunday was sealed by Michael Owen's stoppage time goal and Ferguson immediately described it as one of the greatest derbies of all time, but the Scot was unhappy with the way his defence allowed City to come from behind three times.
"It spoiled a really emphatic victory because we could have won by six or seven and the fact that we made the mistakes probably made it the best derby game of all time," Ferguson said.
"Would we have rather won 6-0 or had the greatest derby game of all time? I'd rather have won 6-0."
United took the lead in the second minute when Patrice Evra poked a pass to Wayne Rooney, who took a touch before stabbing his shot past Shay Given.
But City striker Carlos Tevez, who received a predictably hostile reception from the Old Trafford crowd on his first return to United, had recovered from a knee injury in time to start and played a key role in his side's 16th minute equaliser.
He refused to give Ben Foster time to kick downfield and, as the United goalkeeper dithered, Tevez stole possession before slipping a pass for Gareth Barry to shoot into the empty net.
United regained the lead in the 49th minute when Darren Fletcher headed home a Ryan Giggs cross.
Their advantage was short-lived as Craig Bellamy curled in a stunning long-range effort three minutes later.
Fletcher struck again in the 80th minute with another header, this time from Giggs's free-kick.
City looked to have stolen a point when Bellamy out-paced Rio Ferdinand and squeezed in a 90th minute equaliser.
But Owen, on as a substitute, had the last word when he converted Giggs's pass in the sixth minute of stoppage time.
There was more derby drama in London as Chelsea extended their 100-percent start to the season with a controversial 3-0 victory over Tottenham, while Liverpool lie in third place after Fernando Torres scored twice in a hard-fought 3-2 win at West Ham.
At Stamford Bridge, Chelsea won their sixth consecutive league game under new boss Carlo Ancelotti but their derby triumph wasn't without controversy.
Leading 1-0 through Ashley Cole's 32nd minute goal, Chelsea were fortunate not to concede a penalty when Robbie Keane tumbled under Ricardo Carvalho's late challenge.
Chelsea took full advantage of that escape as Michael Ballack poked in Frank Lampard's pass in the 58th minute before Didier Drogba added a third goal five minutes later.
Liverpool were never behind at Upton Park but were pegged back twice by West Ham.
Alessandro Diamanti scoring a controversial penalty to cancel out Torres's solo opener and Carlton Cole nodding home after Dirk Kuyt had stabbed before Torres hit the winner.
Thomas Vermaelen repaid another chunk of the ten million pounds it cost to buy him from Ajax with Arsenal's first two goals, taking the centreback's tally for his new employers to four after only eight matches, in his side's 4-0 win over Wigan at the Emirates Stadium.
Aston Villa put the pre-match controversy over Nigel Reo-Coker's bust-up with manager Martin O'Neill to one side to claim a 2-0 win over Portsmouth, who became the first side to lose their first six matches since the launch of the Premier League in 1992-93.
Everton defeated Blackburn 3-0 at Goodison Park to claim just their second win in five league games.
Wolverhampton claimed their first home win of the season as Mick McCarthy's men beat Fulham 2-1.
David Nugent marked his home debut for Burnley with a double as the Clarets notched up their third straight win at home with a 3-1 defeat of Sunderland.
A late Matt Taylor penalty salvaged a point for Bolton after Dave Kitson had given Stoke the lead at the Reebok Stadium.
Birmingham took all three points from their visit to Hull thanks to Scotland striker Garry O'Connor's near-post header from a Keith Fahey corner.