La Liga and European champions Madrid won 2-0 on Wednesday night to complete a 5-1 aggregate victory.
Pique, 30, who has been at Barca for nine years, said: “We are not in the best moment, as a team or a club.
“This a long process and there is room for improvement, We must stay as close as possible and keep moving forwards.”
Real were without Cristiano Ronaldo, who is serving a five-match suspension after being sent off in the first leg, and left Gareth Bale and Isco on the bench.
Barcelona, who are lacking in attacking options since the world record transfer of Neymar to Paris St-Germain, scored their only goal over the two legs from the penalty spot.
New signings the key to improvement?
General manager at the Nou Camp, Pep Segura, claims the signings of Philippe Coutinho and Ousmane Dembele are “close”.
Liverpool are adamant that Brazilian playmaker Coutinho, who has submitted a transfer request, will not be sold in this transfer window but Segura has told Spanish television: “We are discussing their deals but do not know when it will be done.”
Borussia Dortmund suspended Dembele after the 20-year-old forward failed to turn up for training.
“We know we have to strengthen this team and that is what we are doing,” Segura added. “We have to help the team.”