Barca impressed in a 4-2 win over Real Sociedad on Sunday in their first match of the new LaLiga season. Pique opened the scoring and Martin Braithwaite found the net twice, while substitute Sergi Roberto scored in added time after Julen Lobete and Mikel Oyarzabal had put La Real back in the game.
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"I don't have to explain what Leo represents, we all know it," Pique told Movistar. "He's the most important player in the history of this club and in the history of football. But all things must pass, we have to keep going. I think we have a good level, we'll be very competitive. I'm convinced we'll compete for all the trophies until the end.
"It's true that Leo not being here means we perhaps won't have the talent we had before. But the team has shown that we're all united. Up front we have goals, and I think at the back, despite the mistake and the free kick [that Real Sociedad scored] we were good.
"La Real played well but didn't create a lot of chances. I think we'll have fun this year."
Pique's goal came a day after the club revealed that the centre-back had taken a "significant" pay cut to allow them to register new signings Memphis Depay and Eric Garcia within the league's strict salary cap. Depay and Garcia were only named on LaLiga's official list of new additions on Saturday night and early on Sunday morning respectively -- but both started for Barca on Sunday evening.
Pique revealed that fellow club captains Sergio Busquets, Sergi Roberto and Jordi Alba also intended to accept wage reductions as Barca adapt to their new financial reality, with this season's salary cap for the club expected to be around €400 million lower than it was two years ago.
"[The pay cut] is what I had to do, I think," Pique said. "I want to stress that we've been in contact with the other captains over the pay cut and I know they'll take the same step shortly, it's just a question of timing. I had to be the first to do it quickly, because of the registration issue. But this is a family, we're all together, the captains have all had the intention from the first moment to adjust to what the club needed, and that's the decision we've taken and we're proud of it."
There were some whistles for left-back Alba from the Camp Nou crowd on Sunday after media reports that he had been unwilling to negotiate a pay cut.
"Sometimes there are misunderstandings," Pique said. "I've been in touch with Sergi, Busi and Jordi, and we've all been aligned, to try to reach an agreement. With hours left before the league started they needed someone to make it official to be able to register the new players, but I know the others are also about to do it.
"Sometimes the information people receive isn't 100% true or it lacks nuance. I wanted to say here that this isn't only my thing, it's all of us, the club has asked for an effort, and they're going to do it."
A crowd of 20,384 was allowed into Camp Nou on Sunday, after over a year of behind-closed-doors games due to the coronavirus pandemic. Barca coach Ronald Koeman praised the fans for their support in the wake of Messi's controversial departure.
"There were only 20,000 people there, but they helped us," he said. "It's important to have the help of the fans. It was a fantastic game, with a crowd, it showed a good image. This is the path to follow. It's good to give confidence to the fans after what happened with Messi."