Fernando Torres gave the Reds the lead at Anfield before French forward Ngog raced through to seal the win in injury-time by coolly slotting the ball past United keeper Edwin van der Sar.
The 20-year-old said the goal was a dream come true, and thanked his team-mates and manager Rafa Benitez for keeping faith with him.
"This was a fantastic moment for me and the team and I would say it's my best moment in football," he told the club's official website.
"I have always dreamed of scoring a goal for Liverpool against Manchester United and now it has happened and it is a really good feeling.
"I dedicate this goal to my family who always support me and the Liverpool supporters. We know how much this victory means to our supporters.
"I also give thanks to my team-mates and the manager for always showing faith in me.
"We know we have a lot of quality so this result means everything for the team. We have worked really hard together and I think we deserved to win."
Ngog will be hoping for a starting berth in the Liverpool team when the Reds take on Arsenal in the Carling Cup on Wednesday, after scoring the winner against Leeds in the previous round.
"We are looking forward to it and all I can do is keep working hard and show what I can do when I get the opportunity," he added.
"I just want to do my best for the team."