The result leaves the Andalusians 19th on 20 points from 32 games, still seven points from the safety zone, after 17th-placed Leganes lost 1-0 at home to Espanyol earlier in the day thanks to Leo Baptistao’s 92nd-minute goal.
Granada have not won a league game since March 1 and 50-year-old ex-Portsmouth manager Adams promised when he was appointed last week that he would "try to achieve a miracle".
His side created few chances against the Galicians, who made 10 changes to the first-choice side that started their Europa League quarter-final, first-leg win over Genk on Thursday.
"Everyone is in pain at the moment in Granada. I met the fans yesterday and it is a very difficult situation but we have to keep fighting, we haven't got a choice,” said Adams.
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"I thought we were very much in the game. If people haven't watched the game and they see 3-0, they probably think it is a very one-sided game but for me it wasn’t."
Granada’s defence fell to pieces for Celta’s opening goal in the 23rd minute, with keeper Guilhermo Ochoa rushing out to head a clearance to Wakaso Mubarak, who lost possession. Claude Beauvue fed Jozabed, who dinked the ball over Ochoa.
Granada's Andreas Pereira, on loan from Manchester United, and Ezequiel Ponce had efforts at goal in the second half but neither troubled Celta keeper Sergio Alvarez.
Marcelo Diaz doubled the visitors' lead with a spectacular free kick in the 73rd and three minutes later Beauvue netted the third after Theo Bongonda’s shot came back off the post.
"It is really important we don't throw the towel in, that we keep fighting, that we keep strong together and go into the next game with hope,” added Adams.
“It's difficult at the moment but there is a bright future. You might not be able to see it right now, but I'm an honest man... We are going to build a football club here, it is just going to take a little bit of time."
In other matches, Valencia held fourth-placed Sevilla to a 0-0 draw at the Mestalla, while Real Betis beat Eibar 2-0.
(Editing by Clare Fallon and Ken Ferris)
