Sir Alex Ferguson's men started brightly, with Gabriel Obertan hitting the post.
But they crumbled soon after, with Jonathan Spector and Carlton Cole both scoring twice each.
It's snow joke for United: Giggs battles with Pablo Barrera at Upton Park
Giggs said: 'Things could have been different had that shot from Gabby gone in.
'We started the game pretty well but that shot didn't fall for us - it hit the post. Then West Ham scored shortly afterwards and that knocked the stuffing out of us.'
Giggs also said United always knew West Ham would provide stiff competition, despite being bottom of the Premier League.
'Whenever you come to West Ham, no matter how they're doing, it's always a tough game and they always want to beat us.
'Even though they're not doing so well in the league, the crowd get behind them and Upton Park is always a tough place to get a result.
Four-midable: Carlton Cole seals West Ham's win with their fourth goal
'It was disappointing to lose 4-0, though. We came here confident we could win the game.
'West Ham played well - you have to give them credit - and they scored some good goals, but we feel we could have defended those goals a lot better.'
Giggs added on MUTV that United would learn from the experience.
'Disappointment can help you. It doesn't feel good at the moment but hopefully the young players who have experienced this can learn from it.
'Next time they're playing they'll be determined to improve their performance and get a better result.
'We're Manchester United and we have to rise above [disappointment]. You have to carry on, keep playing your football and not let your head drop.'
Ferguson hits out at 'soft' Man United as West Ham kill 29-game unbeaten runSpector sparks a blizzard of goals as Fergie is frozen outMANCHESTER UNITED FC