A much-changed Barcelona side fell to a first defeat since November after the Spanish champions lost 2-0 at Celta Vigo while Ousmane Dembele suffered an injury ahead of Tuesday's Uefa Champions League semi-final, second leg against Liverpool.
The win took Celta on to 40 points and a step closer towards guaranteeing survival but it meant 19th-placed Rayo Vallecano became the first team to be relegated, after a 4-1 thrashing at the hands of Levante left them on 31 points from 36 games.
Uruguay forward Maxi Gomez gave Celta a deserved lead in the 67th minute, sliding to the floor to divert a low pass beyond Barca's reserve goalkeeper Jasper Cillessen, after the home side saw a goal ruled out for a marginal offside after a VAR review.
Celta captain Iago Aspas then sealed the win by converting from the penalty spot after another VAR review ruled that Barca's Samuel Umtiti had handled the ball.
Barca's players were given a guard of honour by Celta when they came out of the tunnel before kick off after lifting an eighth title in 11 seasons last Saturday by beating Levante 1-0 at the Camp Nou.
Many of the players who received the tribute, however, had done little to contribute to the title win.
Lionel Messi and Luis Suarez were among a number of high profile players to be rested ahead of the trip to Anfield, where the Catalans are aiming to book their place in the Champions League final for the first time since 2015.
Dembele was one of few regular starters to face Celta but he had to be taken off in the sixth minute after hurting a muscle when attempting a sprint.
Barca said in a statement that Dembele had injured his right hamstring and that he would undergo further tests on Sunday, although the France forward is doubtful for the remainder of the campaign.
Barca, who lost for the first time since a 4-3 defeat to Real Betis nearly six months ago, have 83 points while second-placed Atletico have 74 after losing 3-0 at Espanyol earlier on Saturday.
Valverde put his side's defeat down to the many changes he made.
"We dominated the game in spells but once they scored and they sensed they could win the game we had no response," he said.
"We were playing with a lot of new players and it was difficult for us to create chances. We created barely anything in the second half and didn't do nearly enough to score."
