The 27-year-old was dropped to the bench for the 2-0 La Liga victory, with Javier Mascherano and Jeremy Mathieu preferred at centre-back, although he did replace the former for the second half.
However, ahead of Barca's UEFA Champions League opener against APOEL on Wednesday, Pique refuted reports he had fallen out of favour at Camp Nou, insisting he was happy with Luis Enrique's squad rotation.
"I've never really felt that I was first team or reserve," he said. "We know the season is long. Some games you play, some games you don't.
"He decided that another two players would play instead of me.
"All I can say is I always try to do the best I can and give the best I can to the team.
"There's always things to improve, but if you read the newspapers I need to improve everything."
Pique also revealed that the after-effects of a hip fracture sustained earlier this year were improving with every day.
"My fitness is fine," he continued. "I'm training well - maybe not 100 per cent - but I can play fine as I did in the second half the other day [against Bilbao].
"It's a long-term problem but something that seems to be moving away. It does cause me pain at times but i can train fine - there's no problem in that respect."
Barcelona have opened the new Liga campaign with nine points from three league victories, opening up a six-point advantage over rivals Real Madrid, while defending champions Atletico have seven points.
But Pique does not believe Real will be left behind in the title race.
"We've started well," he added. "We've got nine points and they've lost two games, but that doesn't mean that this is going to be an easy league.
"Real are always going to be there or thereabouts. I don't think we are going to win this league by a wide margin of points."
