Sir Alex was delighted to see his side beat Everton and keep yet another clean sheet, but the United boss insisted there is still room for improvement.
The Reds went five points clear at the top of the league but the 1-0 scoreline made for some nervy moments as the final whistle approached.
“You only need a second to lose a goal,” Sir Alex told MUTV. “And in a situation like today, where Everton kept going and kept playing balls up to the edge of the box, that can happen.
“The aim of football is to kill teams when you’ve got them by the throat and we had Everton by the throat several times and didn’t do that.
“Everton were very energetic and athletic and because we didn’t score a second goal – even though we created some terrific openings – they were always going to carry on and keep fighting. They took us right to the wire.”
In the end, Cristiano Ronaldo’s penalty separated the sides.
“He’s taken his penalty well,” Sir Alex said. “He was under pressure, it was right before half-time… but he remained calm.”
Ronny perhaps should have been given another chance from the spot when Michael Carrick was brought down by Joleon Lescott after the interval. The Reds’ boss certainly thought so.
“That was a clear penalty,” he said. “There’s no question about that. But you’re never going to get two penalties…
“Michael Carrick did well today. His penetrative runs were very good. We’ve spoken about our midfielders making those sort of runs into the box and Michael did that well today.”