It means Moyes' side remain anchored in mid-table, heading newly promoted Hull on goal difference and, amazingly, in points terms, closer to the relegation zone than the top four.
Yet it is hard to condemn United's actual performance on Saturday given they hit the crossbar twice, forced Saints goalkeeper Artur Boruc into a couple of crucial saves and exerted enough pressure to win easily.
For Moyes, it has been the story of a difficult season to date and it is something he is eager to rectify.
"One of the things we will be looking to try and do is finish matches off," he said.
"We have had some opportunities. But I have been saying that near enough from the start.
"We have had quite a few chances and not taken them. Whilst it is like that you are at risk."
Moyes refuted the claim he had created the opening for Southampton's late rally by making the defensive substitution of Chris Smalling for Wayne Rooney in a bid to hold onto what he had rather than push forward looking for a second.
"I didn't think that at all," said Moyes.
"We didn't take the two forwards off earlier. We kept them on, even though we brought Danny Welbeck and Ryan Giggs on.
"We tried to get a second goal. I only made the change in the last three or four minutes when I was trying to make sure we had some height at set pieces."
That Southampton should score from a corner just about sums up the luck Moyes is having at the minute.
Hampered by a wrist injury that will require surgery at some point in the future, United's only significant summer capture, Marouane Fellaini is struggling to live up to his £27.5million billing.
Though he scored his first Premier League goal from open play in two months on Saturday, Robin van Persie appears a shade below his sensational form last term, whilst United's defence looks vulnerable no matter what personnel Moyes elects to use.
In such circumstances, United's worst start since that chronic 1989-90 campaign, which resulted in the club's worst league finish since they were relegated and would surely have got Sir Alex Ferguson the sack had he not managed to win the FA Cup, would be a test even for the illustrious former Scottish manager.
As it is, Moyes remains defiant.
"The players here are good enough," said Moyes, when asked whether he was concerned United would not qualify for next season's Champions League.
"The end of the season is when you have to be in your best form.
"Over the years Manchester United have been slow starters quite often. We have been a little bit slow at the start again but hopefully that will improve.
"We knew we had a difficult opening period and we knew the games we were coming into looked more winnable. But we have got to do it.
"We will pick ourselves up."
United take on Real Sociedad in the Champions League at Old Trafford on Wednesday with injury doubts over veteran defensive pair Rio Ferdinand and Nemanja Vidic, who both missed Saturday's game with minor knocks.
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