Barca could be knocked off from the top of the standings by Real Madrid if Zinedine Zidane's side beat Real Betis in Sunday's late game.
Barcelona went into Sunday's game in the wake of their 6-1 win at home to Paris Saint-Germain on Wednesday in the Champions League, but played without Neymar, and fell behind to a 40th minute goal to Joselu.
Barca lead Real Madrid at the top of the table by a point, but Madrid have a game in hand.
Manager Pepe Mel's side struck first as Joselu gave the hosts a 1-0 lead at half-time in rainy conditions, and Alex Bergantinos followed up with a 74th-minute victor following Luis Suarez's equaliser after the break.
"Only those who has lived what we have experienced this week knows what it all means", he said.
"We knew it would be hard here but what happens before a game always has an impact in the next".
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There are high chances that former Chief Minister Oommen Chandy to be entitled to this responsibility. As he had always stood neutrally to party issues, he was never favoured by any of these groups.
"We let them get into the game for too long in the first half and this is what football is like, when you give a team an advantage they always punish you", Suarez told reporters immediately after the final whistle.
"I have trust in the experience of my players to know that we have a lot at stake", said Luis Enrique on Saturday.
"The opposition played in their own half, they defended well and caused us problems on the counter-attack".
Barca defender Gerard Pique added the comeback against PSG, where they overcame a 4-0 first leg defeat, had taken its toll.
Describing the players as "not machines", the defender also stated his side wouldn't have swapped going out of the Champions League with a win at the Riazor, so they are not too anxious. "Right now we can only concentrate on Deportivo".
"Today was decisive for their battle against the drop and they have achieved that".