The Brazil defender, who is reported to be unhappy about Barca's failure to offer him a new contract, made a costly error in the seventh minute of the match, under-hitting a backpass to goalkeeper Claudio Bravo from which Juanmi scored the winning goal.
Barca enjoyed plenty of possession as they desperately tried to mount a comeback, but Javi Gracia's men held on for their first win at Camp Nou since November 1999.
Alves was later withdrawn in the 73rd minute, but his coach refused to point the finger at him.
"We accept that we may have deserved this defeat," Luis Enrique told reporters. "The entire team is accountable for mistakes - a coach must never single anyone out.
"It was not our best day collectively or individually. Each attack fell apart in the final third against a counter-attacking team.
"We attacked through the middle too many times. We were not very effective or decisive. If you have problems [in attack] then this [a failure to score] happens.
"It's a result that hurts us and is not good for us. Malaga played a very good match."
