Pique went out with a tirade of expletives towards referee Jesus Gil Manzano on Tuesday, although he insisted the referee's version of events is not entirely true and refutes some of the insults he is charged with saying.
The former Spain international also spoke about his respect for Real Madrid president Florentino Perez but expressed surprise at how he handled the failed launch of the European Super League last year.
"I'm sure it will appeal to me at one point but not right now," Pique told Ibai Llanos on Twitch on Wednesday in a wide-ranging interview, the first since he announced his retirement from football last week.
"Not training every day will give me the opportunity to focus on other things. In the future, we will see, but I would like to help the club of my life maximise the potential it has."
Pique, 35, is already the owner of second division side Andorra, who he said he can now give more attention to, and through his company Kosmos is also involved in various other projects, including the tennis tournament the Davis Cup and various esports endeavours.
The defender's final game for Barca ended with a half-time red card against Osasuna on Tuesday, meaning he was unable to come on for what would have been the 617th and final appearance of his career with the Catalan club.
Gil Manzano's report after the game detailed how Pique had launched a wave of abuse against him, but Pique said the referee's explanation is incorrect and added that it was a teammate who shouted the most extreme insult.
"I went to talk to him about various moments in the game, saying that he had screwed us and, at that moment, he sent me off," Pique said. "I had not said anything else at that moment and he dismissed me.
"His report is not right. I did not insult him or anything. Then, once sent off, I go into the dressing room, which is next to the referee's dressing room, and a teammate shouts the phrase that is in his report. And the referee hears that next door and puts the words in my mouth."
Before Tuesday's 2-1 win at Osasuna, Pique had played what was his final game at the weekend against Almeria at Camp Nou. He said he could never have expected the send-off he received from a season-high crowd of other 92,000, adding that he would have retired earlier this season if Barca had not suffered so many injuries in defence.
"Saturday was spectacular for me," Pique said. "I was not giving too much importance to it, but I am so grateful to get a send-off like that and to realise the appreciation the fans have [for me].
"There were a lot of reasons [for retiring] which I had been thinking about throughout the season. I spoke with Xavi at the start of the campaign and he told me it would be difficult for me this year, but I wanted to give it a go. Last year had been good for me personally.
"But the sensations were not good in general. There were moments I thought about retiring earlier when I was not playing. After one game, I was doing the post-game session at Camp Nou for players that had not played and I thought about going into the dressing room and calling it a day.
"In the end, with the injuries we had in defence, I delayed the decision but now, with the World Cup break, felt like a good moment."
Whatever he does next, Pique is likely to remain linked to football in one way or another. Coaching does not seem a path that he will follow, with his inspiration coming more from those at the top of the game, including Madrid president Perez.
But despite the respect he has for Perez, Pique described the launch of the European Super League as "a big f--- up" -- although he acknowledged change is needed to keep younger fans gripped.
"The presentation for the Super League was a big f--- up, above all coming from Florentino," Pique said. "I hold him in the highest regard, so I was surprised how they screwed that up.
"The presentation on [Spanish TV programme] El Chiringuito and all of that, I did not understand it. I am sure he wanted to achieve something, but I don't know what. But I agree with him about needing to captivate younger audiences, even if I don't agree with the Super League.
"I think we have to change the established rules that we have had for years. We have to have shorter, more seductive products. To me, 90 minutes seems a long time. If not that, they need to change something. Football is still the king of sports, but for me it is outdated."