A 1-0 defeat to Athletic saw Barcelona knocked out of the Copa in the quarter-finals on Thursday, with that familiar route to silverware now cut off to the 30-time winners.
The setback followed criticism from director of football Eric Abidal, who questioned the team's effort under former head coach Ernesto Valverde, which led to a rebuke from star man and captain Lionel Messi.
"It's not time to air the dirty washing. The dressing room is fully united," Barca defender Pique told reporters. "Elimination is a big blow but we said in the dressing room that we've taken a step forward and played well, despite all the noise that's been generated."
He added, according to several Spanish newspapers: "We have to focus on playing and winning. We have to return to winning ways. The players have the ability to keep winning and we are working on that every day, finding a better feel for the game."
With LaLiga and the Champions League still in their sights, Pique said of Barcelona, who are three points behind Real Madrid: "There is enough confidence and talent to be able to win the two remaining titles."
Pique hobbled off in the second half in Bilbao with what initially appeared to be a groin injury, but he said the blow was to his adductor and "not serious".
Club president Josep Maria Bartomeu said Barcelona looked to be on the right track, after a match they could easily have won.
Messi and Antoine Griezmann missed clear chances before Inaki Williams headed the winner deep in second-half stoppage time.
"The first thing is to congratulate Athletic, who will be in the semi-finals, but I also thank the Barca fans who have come and I also congratulate the Barca players because they fought, dominated and played well. [Athletic] have only had one chance and they scored," Bartomeu told Barca TV.
He said that he appreciated Barcelona's "performance and ambition".
"The ambition and the attitude that I saw on the pitch encourages me with a view to LaLiga and the Champions League, so successes can come," Bartomeu added.
"I repeat that we had clear occasions, such as those of Griezmann and Messi, and we dominated. Now we focus on LaLiga and the Champions League, but I want to emphasise the ambition, the attitude and the work done. We deserved to go through."
Barca midfielder Sergio Busquets said, according to AS: "It is a sad day for everyone. We have two competitions that we have to keep fighting in. This does not stop, we have to continue, we have done things well and we have had the game quite under control. In an isolated play at the end we are out of the Copa."