Needing a result in Istanbul, the Liverpool got off to the worst possible start when a close-range shot by Serdar Ozkan deflected off Reds defender Sami Hyypia into his goal in the 13th minute. The own goal unfolded after a clearance rebounded off Steve Finnan into the path of Serdar.
Brazilian striker Bobo iced the Besiktas victory in the 82nd minute. Steven Gerrard scored a consolation goal three minutes later for Liverpool.
Liverpool manager Rafa Benitez remained optimistic about the Reds' chances of finishing in the top two and advancing to the final 16.
"These situations in football can happen," he said. "We have to keep doing the right things and see what happens. We can't do anything more. The performance was OK."
Gerrard wasn't quite so positive about Liverpool's chances.
"We had a mountain to climb before this game," he said. "We have an even bigger one now."