Josep Vives admitted Barca had been left irritated by the Brazilian's decision to leave despite signing a new five-year deal last year as PSG paid his 222 million euro ($264 million) buyout clause to leave Barca powerless to prevent Neymar moving on.
"Any separation causes annoyance, especially when it is one not wished for by the club due to a unilateral decision on the part of the player," Vives told a press conference at the Camp Nou.
Barca had deposited the bonus with a notary to be paid on September 1 had Neymar remained at the club, but have already recovered the 26 million.
During his presentation as a PSG player on Friday, Neymar said that "at no point did I lack respect to the supporters or the club" in deciding to bring to an end his four years in Catalonia.
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However, Vives insisted Barca are unhappy with the way in which his exit came about.
"There is annoyance at the decision, but also the way it came about."
"He is a great player, we have enjoyed him a lot, but the world doesn't end after Neymar," he added.
"It is not the first time that we have gone through a situation like this and the club has continued, grown and become more universal."
The move is not just a huge blow for Barca's prospects on the field, but their prestige as one of the world's richest and most successful clubs.