Supporters booed and harassed the team during a training session this week, while the federation of Deportivo supporters clubs issued a statement demanding more effort from the players.
The Galician side host Granada on Saturday night, and Paciencia urged his team to improve on their last performance, the 3-1 defeat to Getafe the previous weekend, which he labelled "the worst game we have played since I arrived".
"The fans want to win and we need to do more, we have to get back to where the fans want us to be," he told reporters.
"We know that the supporters clubs have reason to be angry, they are really suffering at the moment, and we are having a bad time of it too. We want to start winning again so that the fans can be happy with us."
The Portuguese coach admitted he would have liked to have strengthened his squad in the January transfer window, but was unable to do so due to the club being in administration.
"I think we have good players and we have quality, but we don't have a very balanced squad because our financial situation is not ideal to build a team," he said.
However, despite the squad's shortcomings, Paciencia believes the players he has are good enough to lead the team out of the relegation zone.
"It's possible to stay in the top flight with the squad we have, even though we are all suffering with everything the team is going through," he said.
"But if there is a way of changing it all, it is to beat Granada on Saturday and start moving up the table, which is what we all want."
Tomorrow's match will be Lucas Alcaraz's second game in charge of Granada since being appointed coach less than two weeks ago.
His second spell in charge of the Andalusian club got off to the perfect start last week with a 1-0 win over Real Madrid, and although he acknowledged the game with Deportivo would be different, he warned it would be no easier.
"Every game is difficult, and they are approaching every game like it's a final," he told a press conference.
"We'll have to match them from the start and go looking to take charge of the game, following a number of guidelines, above all maintaining intensity and keeping concentration."