The only goal of the game fell to Rufete on 34 minutes, whose shot took a wicked deflection off Sami Hyypia to beat Jerzy Dudek.
As Liverpool piled on the pressure in the second half, bringing on Milan Baros, Vladimir Smicer and Bruno Cheyrou for Danny Murphy, Emile Heskey and Jamie Carragher, they created more chances but Valencia held firm.
With Basle set to play their postponed match against Spartak next week it remains to be seen whether a win will be required if Liverpool are to progress.
Valencia are confirmed winners of Group B.
Liverpool: Dudek, Riise, Traore, Hyypia, Carragher (Cheyrou 81), Murphy (Smicer 60), Hamann, Diao, Gerrard, Heskey (Baros 61), Owen.
Subs Not Used: Kirkland, Babbel, Diouf, Biscan.
Valencia: Canizares, Curro Torres, Marchena, Pellegrino, Carboni, Rufete, Albelda, Baraja, Gonzalez (Vicente 87), Aimar (Angulo 68), Carew (Mista 79).
Subs Not Used: Palop, Aurelio, Djukic, Sanchez.
Booked: Albelda, Mista.
Goals: Rufete 34.
Attendance: 41,831.
Referee: Terje Hauge (Norway).