The Red Devils were held away by 10-man Southampton at St Mary’s in the early kick-off on Saturday afternoon.
Daniel James’ stunner was unable to inspire Manchester United as they were forced to settle for a 1-1 draw on the south coast.
United have an outstanding record at St Mary’s and Ole Gunnar Solskjaer’s men looked on course for a first away win since their jaw-dropping Champions League triumph at Paris St Germain.
But the visitors were unable to build on James’ beautiful early strike and Vestergaard levelled after the break, with Saints holding on for a draw despite Kevin Danso’s sending-off leaving them under the cosh.
And Solskjaer believes his side lacked the cutting edge to claim all three points.
“Well I thought we started well of course,” he told Sam Matterface. “We got the first goal and the game is there for us to be won.
“But we’re not ruthless or clinical enough and we kept giving the ball away in dangerous areas, which then created an atmosphere here.
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“It gave them encouragement and we couldn’t find the second one which would have finished the game.”
United have managed to keep one clean sheet in their last 19 games in all competitions, have won just one of the last nine Premier League games and not won away from home since that famous win over Paris Saint-Germain.
Solskjaer convinced the board to part with £80million to sign Harry Maguire from Leicester City, but defensive frailties are still evident.
But the Norwegian believes they have everything in place to build upon.
“Well you want to have a foundation to build on,” Solskjaer added. “The thing is; if we keep getting battered and chances and chances and chances, then there is loads of work to be done.
“But we are on the right track; we are not conceding many chances. Palace had two last week, scored two.
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“Southampton had one 10-second period where they could have scored and we conceded so the concern isn’t the amount of chances we are conceding.
“The concern is that they are very efficient and they score.”
The opening day thrashing of Chelsea feels like a lifetime ago, especially considering a draw at Wolves was followed by defeat at home to Crystal Palace.
United welcome Leicester City to Old Trafford next weekend, before beginning their Europa League campaign on the Thursday after that.