Jordi Mestre said the Brazil forward, 25, played “cat and mouse” with the club before his exit in August.
PSG paid €222m for Neymar, making him the most expensive player in history.
“We would have saved a lot of money and a lot of media noise,” said Mestre.
“What hurt me the most was the way it happened.”
Neymar signed a new five-year deal at Barcelona in July 2016, which included €8.5m renewal bonus.
Mestre said, “If he came to us and said, ‘I want to go’, we would have reached an agreement. What you can’t do is rock the boat.
“He told us nothing. If he had done, PSG would have been able to buy him for less money and it would have cost us less to sign players too.”
Neymar said at the time of his move that he had “followed his heart”.
“The decision was difficult to take,” he said. “I didn’t come for the money. I came for the motivation and the challenge.”
Since Neymar’s departure, Barcelona have spent £142m on signing Philippe Coutinho from Liverpool, having brought in Ousmane Dembele from Borussia Dortmund for an initial £97m, which could rise to £136m.
Following Neymar’s departure, Barcelona said they would withhold a further 26m euro (£23m) loyalty bonus.
“It arrived at a point where we saw where things were going, so we told him we would not pay his contract renewal loyalty fee,” said Mestre.