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Spain were beaten 2-0 by Italy in the last 16 of Euro 2016 on Monday and Pique believes they should no longer be considered favourites for tournaments.
"I think we have to undertake a big reflection, in terms of style and level," the 29-year-old said.
"We don't have the level that we had a couple of years ago."
The Barcelona centre-back added: "We are a team that can win matches because of our name and our past, but we are not the best team. We are not in a position to win tournaments right now.
"It's not only about the level of the players. Despite trying to play the same way as we have done in recent years, we weren't as effective.
"This exit could help us to go into future competitions knowing that we are no longer favourites to win."
Manager Vicente del Bosque has said he will consider his future following Spain's exit.
He took over after Luis Aragones had led the side to their first major trophy with the 2008 Euros, adding Spain's first World Cup in 2010 and claiming victory again at the Euros in 2012.
Del Bosque offered to resign after Spain's exit at the 2014 World Cup group stage but was convinced to stay, and has previously indicated he plans to retire after the Euros.
"I must speak to the (Spanish federation) president," Del Bosque. "We must do what is best for Spanish football.
"I don't think an era has ended. Spanish football is very well structured. There are good academies, very good players and very good clubs."
Compiled by BBC Monitoring
El Mundo examines how Spain's tournament went day-by-day in a "diary of an unexpected failure" that takes in the Torbe sex scandal allegedly involving David de Gea, Chelsea attacker Pedro disturbing the peace, and Sergio Ramos missing a penalty.
El Pais describes the defeat against Italy as having closed "Spain's great cycle". It goes on to say that despite the loss, coach Vicente del Bosque has become a reference point for Spanish football. "If he resigns or is forced to resign, his legacy will remain for life."
Barcelona-based daily El Periodico de Catalunya says the defeat is "the end of a glorious era". The report goes on to say: "Italy, a bold a beautiful Italy... closed the circle of sad Spain, which returns home dejected. Everything in life has an ending."
The playing style that saw Spain win the 2010 World Cup and successive European Championship titles may no longer work, says Gerard Pique.