Anelka was outstanding in the comfortable win for the visitors.
Bramble told safc.com: "When they play like that they are going to get the win against most teams in this league.
"Before they scored the third goal I thought maybe we could hold them off. We knew they'd create chances.
"It was backs to the wall at times; we rode our luck and when you do that sometimes it can turn out to be your day. But it was a fair result in the end.
"Anelka was the best player on the pitch. He's so intelligent when he sits in the hole. He has a great footballing brain and we couldn't get near him."