With many of his players in action with their international sides in midweek, coach Luis Enrique rotated his squad, resting regulars Luis Suarez, Andres Iniesta, Gerard Pique, Sergi Roberto, Jordi Alba and talisman Lionel Messi.
The decision backfired and Alaves, playing in the top flight for the first time in a decade, made the most of their few chances, frustrating the champions even after Suarez, Messi and Iniesta came on.
Ibai Gomez's 64th minute strike won the game for the Basques after Jeremy Mathieu had cancelled out Deyverson's surprise opener.
"We made a lot of changes so the freshest players could play but we were fragile in defence and we have to look at that," said Luis Enrique.
"Conceding the second goal after an error of ours was a big blow for the players but on Tuesday we're playing the Champions League and that's another story. In that competition you pay dearly for your errors."
Luis Enrique is expected to field his first choice 11 against Celtic, so Suarez will meet up with his former Liverpool manager Brendan Rodgers.
Rodgers presided over the Uruguayan's best two seasons in England, compelling Barcelona to pay the Merseyside club 81 million euros ($90.97 million) for him in 2014.
Goalkeeper Marc-Andre Ter Stegen is the coach's only doubt after he missed the Alaves game with a muscle strain.
Celtic head to Spain on a high after thrashing Glasgow rivals Rangers 5-1 on Saturday in the first league Old Firm derby in over four years to stay top of the Scottish Premiership.
Rodgers is still without lead striker Leigh Griffiths through a torn hamstring injury but new signing Moussa Dembele proved more than an able replacement against Rangers, scoring his first professional hat-trick.
Celtic were beaten 6-1 on their last visit to the Nou Camp in December 2013, but Dembele believes they can get something this time.
"We are going there to give everything and try to get a result," he said.
"When you start a game of football, even if it’s against the best team in the world, you have to go there and show what we can do and give everything to try and get a result."
(Reporting by Richard Martin; editing by Clare Lovell)
