Pipping rivals Real Madrid to the title looked to be Barca's best chance of salvaging what had been a disappointing campaign although Wednesday's remarkable 6-1 win over PSG, which took them into the quarter-finals of the Champions League, has given them belief of a second treble in three years.
"We have never been cautious and we want to win the three competitions," said Luis Enrique, whose side will play Alaves in the King's Cup final in May.
"It's a shame that we have to get back to work immediately as the players would like to have time to celebrate this with their families but we have to get back to training because if we have one bad game we'll get beaten. You always have to improve."
Barca have won their last six league games and scored 17 goals in their last three in all competitions, although Deportivo have improved under new coach Pepe Mel and should provide a sterner test for the Catalans than their last visit to Riazor, where they won 8-0 last season.
The former West Bromwich Albion and Real Betis manager Mel is unbeaten in three games with Deportivo, overseeing draws at home to Atletico Madrid and Betis and a win over Sporting Gijon since Gaizka Garitano was sacked following four straight losses.
Barca lead Real by one point in the standings although Zinedine Zidane's side have a game in hand and will be ready to pounce on any slip up by the champions when they host Betis, who they thumped 6-1 in October.
Betis have won just two league games in 2017.
Real also reached the Champions League quarter-finals by seeing off Napoli 3-1 on Tuesday to cap a 6-2 aggregate win over the Italians although Zidane faced renewed questions about his team's style of play after a torrid first half in Naples.
The front three of Karim Benzema, Cristiano Ronaldo and Gareth Bale struggled to click, making just seven passes between themselves, and it took two headers from inspirational Sergio Ramos to turn the game back in Real's favour after they trailed 1-0 before the break.
Zidane, who has a habit of keeping his cool in public appearances and calmly swatting away criticism about his side, said he was not overly concerned by his side's display in the fervent atmosphere of the San Paolo stadium.
"I'm not worried by our first half even though it's true we should have done better," he said.
"When you play at a ground like this you'll always have problems but we were much better in the second half."
(Reporting by Richard Martin; Editing by Alison Williams)
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