Forward Messi requested a transfer this summer, believing he could leave for free according to a clause in his deal.
The club’s all-time leading scorer ultimately opted to stay, partly to avoid a potential court case.
“We should preserve our figureheads, not underappreciate them,” Pique told La Vanguardia newspaper.
“It’s all too confrontational. What’s going on? Messi deserves everything; the new stadium should be named after him first and then the sponsor.
“I ask myself: How can it be that the best-ever player to have played the game, who we have been lucky enough to enjoy, wakes up one day and sends a Burofax (recorded delivery mail) because he feels like he’s not being listened to?”
The details of a clause in Messi’s contract proved crucial to his situation this summer.
The Argentine, 33, says the fact he did not tell Barca he wanted to leave before 10 June meant that any prospective club would have to meet his 700m euro (£624m) release clause, instead of paying no fee.
Messi’s decision to leave came after a disappointing season for Barcelona, which saw them finish second to Real Madrid in La Liga and humiliatingly crash out of the Champions League in the last eight courtesy of an 8-2 defeat by Bayern Munich.
They hired Ronald Koeman as manager and attempted to freshen up their squad in the summer but have had an inconsistent start to this campaign, with last weekend’s shock 1-0 loss to Getafe leaving them ninth in La Liga.
Pique’s comments come just a day before the first El Clasico of the campaign and two days after the 33-year-old centre-back signed a new three-year deal at the club. He was sent off near the end of this week’s Champions League win over Ferencvaros.
A vote of no confidence against the board, led by president Josep Bartomeu, is also believed to be imminent.
Pique addressed media reports that Bartomeu knew that the club had hired a social media agency to criticise the players earlier this year – allegations which Bartomeu denies.
“I, as a Barca player, see that my club have spent money, money they’re now asking us for (in salary reductions), to criticise us – and I’m not talking about criticising people outside the club, but current players – it’s atrocious.
“I asked (Bartomeu) for an explanation and he said ‘Gerard, I didn’t know about it’, and I believed him. But then you see that the person who was responsible for doing this is still working at the club.
“That hurts me a lot. And I’m saying that here because I’ve already said it to the president, too.”
‘Griezmann has chance to play’
There are fitness doubts over forward Antoine Griezmann, who stayed on the bench for Barca’s victory over Ferencvaros.
It was not clear whether the Frenchman had been dropped or rested for the 5-1 win.
“He has a chance to play,” said Koeman. “But it’s not good to discuss his role for every game.”
Jordi Alba has been included in the squad after recovering from a hamstring injury but it remains to be seen if the left-back is deemed ready to start.
“Always the last word is with the player,” said Koeman. “If there’s no reaction he has a good chance of playing tomorrow.”
Real Madrid boss Zinedine Zidane said defender Sergio Ramos will be available to face Barcelona after recovering from the knee injury that kept him out of the loss to Shakhtar Donetsk on Wednesday.
“Sergio is our captain, our leader,” said Zidane. “He’s recovered, he’s going to be with us. It’s about being one hundred percent though and I think that Sergio is already there.”
Zidane insists he has Real support
Zidane also insisted that he has the full support of Real Madrid president Florentino Perez and called on his players to turn their season around by beating Barca on Saturday.
Madrid and their coach head to the Nou Camp under pressure after consecutive defeats to Cadiz in La Liga and Shakhtar in the Champions League.
Asked if he still feels the backing of the club and president, Zidane said: “Yes, from everyone. I have won many things with these players and I will always be with them to the death. I will always be with them.
“But we have to change our momentum, we have had two difficult games, and that’s what this is all about.
“There are always bad moments but there are those teams in those moments that show their character and quality. We have to do that tomorrow.”