Paraguay striker Nelson Valdez netted either side of half-time for the tiny Alicante-based club to seal one of the biggest upsets of recent seasons and inflict the first home defeat on Pep Guardiola's side since May 2009.
Alves, whom Guardiola left out of his starting XI along with World Cup-winners Xavi, Sergio Busquets, Pedro and Carles Puyol, noted that Barca's most successful season, in 2008-09, had also started badly.
They lost their opening La Liga match 1-0 at Numancia and drew their second 1-1 at home to Racing Santander before going on to seal an unprecedented treble of Spanish league and cup and European Champions League.
"We shouldn't get angry and lose heart," Brazilian Alves told a post-training news conference.
"It's not about how you start but how you finish.
"There was a lot of criticism at the beginning of the club's most successful year ever and it ended very well. Hopefully we won't ultimately need these points we have dropped now."
Barca lost only once on their way to setting a record points tally last season, going down 2-1 at Atletico Madrid, whom they play in the Spanish capital next Sunday.
Alves put Saturday's reverse down to a bad day at the office and said it was better to get defeats out of the way early in the campaign.
Barca were not about to change their playing philosophy of trying to win and entertain at the same time, he added.
"We have our way of doing things and we are not thinking of tinkering with it," he said.
"It's not just a matter of scoring a goal and getting the points but playing to win and enjoy ourselves."
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