The Premier League leaders scraped a 2-1 win on Wednesday night to go seven points clear at the top and the manager put much of the blame on a worse-for-wear Old Trafford pitch
Saints took the lead in the first five minutes when Jay Rodriguez pounced on a poor backpass by Michael Carrick and rounded a helpless David de Gea.
United hit back soon after through Wayne Rooney before the England international secured the win with his second but the visitors dominated proceedings following half-time and Sir Alex concedes that his team rode their luck at times.
Speaking to MUTV, the Scot remarked: "In my experience at the club, when we're going for championships there's always a game where you say to yourself: 'we were a bit lucky' and I think this was one of those nights.
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"On that surface the players are trying to take a touch, play their football and they found that difficult."
Sir Alex noted one major factor of his side's poor second-half performance, lamenting the state of the Old Trafford pitch on the back of a period of adverse weather in the area.
He continued: "In the second half, the players just found the pitch impossible. We tried to play the way we normally play and found it difficult because the pitch had dried out a lot. It was an ice cold night and it happens.
"First half, we lost an early goal but it didn't deter us from playing some fantastic football and we could have been four or five up at half time, but once the pitch started to dry out the players found it difficult to play a different way and it really required us to play the ball into the gaps, which we don't normally do.
"The pitch didn't help us. We can't use that as an excuse, but it didn't help us. It's a worry. We've won the game and I think that's the one thing we can take out of it."