Sir Alex Ferguson's team came from behind to win against ten men, with Rafael scoring a fine goal and Robin van Persie grabbing the winner from the penalty spot after Jonjo Shelvey had earlier been sent off for a strong challenge on Jonny Evans.
Steven Gerrard opened the scoring for Liverpool despite their man disadvantage and Giggs praised Brendan Rodgers' team for making it difficult for the visitors.
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"It's always tough to play against a team like Liverpool. They keep the ball well, and even if they go down to ten men they don’t change, they keep the ball and that's always tough.
"The crowd got up and we didn't play well, we didn't keep the ball well enough. It was great to see Rafa [Rafael]'s goal go in and that probably lifted us."
Before the game both sides took part in an emotional tribute to the victims of the Hillsborough disaster, but Giggs didn't think the United players were affected by the poignancy of the occasion once the game had kicked-off.
"I think it's just a tough place to come," he reflected. "Liverpool obviously wanted to put in a performance because of the occasion, and they did that. I think Liverpool made it tough for us but we could've played better."