The 27-year-old struck twice in the opening period to give Sir Alex Ferguson's side a dream start, but goals from Yaya Toure and City skipper Pablo Zabaleta hauled the hosts level before Robin van Persie's last-gasp free kick flew in courtesy of a deflection from Samir Nasri.
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"Wayne is the kind of player who can score goals but if someone is scoring more, he's not too bothered," Giggs told the Sun.
"He's quite happy setting goals up and pitching in with important goals like he did on Sunday.
"It's like when Cristiano [Ronaldo] was here. He scored a lot of goals but, like Wayne, he's not just an out-and-out goalscorer. He's more than that. Wayne is the catalyst to everything good that we do. He can score goals and make goals."
Rooney and Van Persie have formed a formidable partnership since the latter's arrival from the Emirates Stadium, helping United to reach the Premier League summit and also cruise through the Champions League group stage, but Giggs insists he expected the Dutchman to make an immediate impact.
"Robin has not surprised me because at 29 I knew he was a ready-made, experienced, world-class player," he added.
"But he just has that bit of class that can make a difference like it did on Sunday. You see it in training, you see it in games, he's just a brilliant player."