United prevailed at St Mary's on Monday despite an error-strewn display in which they mustered only three attempts at goal, with Van Persie netting either side of Graziano Pelle's first-half equaliser.
It gave United a fifth consecutive win and sent them up to third place in the Premier League ahead of Sunday's home game with old enemies Liverpool, but Van Gaal admitted that his team had been ‘lucky’.
"I think that not only the goals are telling about Van Persie, but also his performance — he was one of the three players on the pitch for United who were good or maybe very good."
Van Gaal refused to reveal the identities of the other two players who had met his expectations, and when asked for his verdict on the other United players, he replied: "They were not good”.
However, he added that even though it was now ‘fantastic to be third on the table’, they had merely been a ‘lucky team’.
In contrast to United, Southampton, who slipped to fifth, created a glut of opportunities, forcing visiting goalkeeper David de Gea to make three impressive reflex saves.
Southampton manager Ronald Koeman has now seen his side lose three games in succession after previous defeats to Manchester City and Arsenal, but he felt the latest setback was largely self-inflicted.
"We did not lose against United tonight — we lost by ourselves," he said. "City were the better team, but we deserved more against Arsenal, and we deserved much more tonight.”
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