Pique's unfortunate mistake handed Madrid the lead in the first leg at Camp Nou on Sunday before further goals from Cristiano Ronaldo and Marco Asensio secured a commanding 3-1 advantage, after Lionel Messi's penalty had levelled the scores.
Segura stated afterwards that the error by the centre-back "changed the game completely" but Busquets has defended his team-mate and insisted it was wrong for a club official to criticise a player in public.
"It was an unlucky incident. We lost 3-1 because we made a number of errors and they were very good at the critical points," Busquets told a news conference ahead of Wednesday's second leg at the Santiago Bernabeu.
"We didn't lose because of a single piece of play. It's not the best way to express yourself and even less so from within the club, aimed at a player.
"We knew what could happen from the start of the game. We had a good first half, but after their goal we opened up and we couldn't change things with the equaliser.
"When they have space, and on the counter-attack, they're almost unstoppable.
"We don't give up the trophy as lost. It's difficult but we have to keep believing as a team. We have to be good defensively.
"Scoring three goals won't be easy but we've done it there plenty of times."
Sergio: "In a Barça-Madrid anything can happen, we are two great teams. The more in form will win" FCBlive pic.twitter.com/lWrGZEdjjo— FC Barcelona (@FCBarcelona) August 15, 2017
Barca beat Madrid 3-2 in the International Champions Cup in pre-season, with Neymar picking up two assists in what proved to be his final appearance for the club before his world-record €222million move to Paris Saint-Germain.
However, Busquets insists that the forward's departure cannot be used as an excuse for Barca losing important matches.
"With Neymar's exit, the team have lost something attacking-wise. That's obvious," he added.
"We will have to have more attacking players who can carry the weight of the game. Neymar's exit can't be an excuse."
Barca confirmed on Monday that they have agreed to sign Paulinho from Guangzhou Evergrande Taobao for €40m, although the Brazil international will not be available for Wednesday's game.
The 29-year-old's move has been met with a mixed reaction but Busquets is confident he will improve the team.
"He has a different profile. He can contribute a lot because he's first-choice for Brazil," he said. "He will bring a lot to us and we welcome him with open arms."