The Catalans had the opportunity to reduce their deficit to leaders Real Madrid to just four points with a victory in Pamplona but now look set to find themselves 10 points in arrears, with Los Blancos hosting Levante at the Santiago Bernabeu on Sunday evening.
However, Pique insists that Barca are not yet ready to throw in the towel and called on the club's fans to keep the faith.
“We aren’t giving up on La Liga," the Spain international is quoted as saying on the club's official website.
“The points difference keeps growing, but I ask the fans to stay by our side because we need them more than ever."
Barca had found themselves two down after just 22 minutes in Pamplona, with Dejan Lekic notching twice for the hosts.
Alexis Sanchez pulled a goal back for the reigning champions in the second half only to see Raul Garcia post a swift riposte for Osasuna to restore their two-goal advantage.
Barca got back to within striking distance again when Cristian Tello scored with 17 minutes remaining and they looked to have equalised when Alexis found the net once more, but the Chilean was controversially ruled offside.
Despite the debate over whether the winger's goal should have stood, Pique admitted that Barca only had themselves to blame for the damaging loss and argued that they must now look to put things right, starting against Bayer Leverkusen in midweek.
“The referee’s performance isn’t an excuse for losing to Osasuna," the centre-back stated.
“The Champions League is a very attractive competition, the most prestigious; we’ll give it our all to try and win it."
Barca travel to Germany on Tuesday evening before returning to Camp Nou to take on Valencia in La Liga on Saturday night.
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