Carrick's weak back-pass was compounded by David de Gea's failure to block, allowing Jay Rodriguez to give the Saints a second-minute lead.
It didn't prove too costly as Wayne Rooney's double put United ahead before the break and then some backs-to-the-wall defending after the interval allowed the hosts to claim a 2-1 win that sent them seven points clear of Manchester City.
"Michael's pass-back was a bit soft and Michael held his hand up - its great to see that, honest players like Michael saying `Sorry boss, sorry lads'. It's great," said Ferguson.
Ferguson cited a chronic playing surface for his side's dismal second-half performance, although he insisted it should not be used as an excuse and that Southampton's second-half display was the best he had come across at Old Trafford all season.
"In the second half Southampton produced the best performance anyone has done here this season," he said.
"They pushed right on top of us and didn't give us time to settle.
"But my experience of this club, when you are going for championships, is that there are always games where you can say we were a bit lucky. This was one of those nights."