Daniel Agger had put the hosts ahead on 21 minutes, before Ji-sung Park fired a brilliant equaliser six minutes before the break.
The game looked to be heading for a replay at Old Trafford before Dirk Kuyt stole in to blast home the winner with two minutes remaining.
"I don't know how we lost it," the boss told MUTV and ITV1. "It was a really good performance from us.
"That can happen in the FA Cup though - you can have one bad break against you and you lose the game. It's a sudden death situation which we've experienced many times over the years and anything can happen. It's a bad blow though because we didn't deserve that.
"I'm pleased with my players. They performed very well, dominated the game and played good football," added Sir Alex. "They didn't deserve to be beaten at all. We maybe should have won the game - we were the better team.
"But that's FA Cup football I'm afraid and it's not the first time it's happened. To lose it is a devastating blow."
The Reds had looked in control for the most part with plenty of possession and one or two decent sights of goals. Sir Alex felt United's good play deserved better reward, but ultimately he was disappointed with the goals his side lost.
"Both goals were avoidable. We didn't do well - we had too many defenders in and around the goalkeeper for the first one and the second one was just one of those lucky breaks you get," he