"It was one of those days," said Williams, who double faulted six times. "I wasn't really happy with the way I was playing. I just wasn't happy out there today in general.
"I think I woke up on the wrong side of the bed."
While Serena advanced, her sister Venus lost 6-2 5-7 7-5 to Germany's sixth seed Angelique Kerber in a tense battle under the lights following Federer's dominant triumph.
In Image: Serena Williams looks into the stands during her match against Spain's Maria Jose Martinez Sanchez