Barcelona were "naive" and "disrespectful" in how they handled Ernesto Valverde's sacking, according to Rivaldo.
Valverde's three-year reign at Camp Nou came to an end on Monday when the club decided to relieve him of his managerial duties.
The Blaugrana announced ex-Real Betis boss Quique Setien as his successor, on a deal set to run through to 2022.
Valverde guided Barca to back-to-back Spanish titles, but a number of high-profile failures in cup competitions ultimately undermined his achievements in La Liga.
The 55-year-old was heavily criticised after a Champions League semi-final defeat to Liverpool last season, which was followed up by a Copa del Rey final loss against Valencia.
Barca were also beaten in a Supercopa de Espana semi-final tie by Atletico Madrid last week, which proved to be the final nail in the coffin for Valverde.
Rivaldo believes the Spanish champions could have avoided a disruptive changing of the guard had they lined up a "back-up manager", with club legends Xavi and Ronald Koeman thought to have turned down the chance to return to Camp Nou.
"It's clear that Barcelona didn't deal well with this change of manager," the ex-Barca midfielder told Betfair. "They were a little naive and perhaps disrespectful with Valverde; it is never a positive action to start negotiating with a new manager while the current one is still working.
"Of course, Xavi and Ronald Koeman rejecting their proposals also added to that problem creating lots of speculation, before they finally announced Quique Setien.
"Football is a cut-throat business, of course, but we all know that the process wasn't well driven by Barca's board. Clubs like Barcelona or Real Madrid should always have back-up managers in order to avoid such situations.
"Yes, it isn't pretty to talk to other managers before really wanting to sign them, but if you manage to identify one or two realistic targets who probably accept an offer when it comes, you can avoid these kind of tough situations."
Rivaldo went on to express his belief that Xavi will "wait for the right moment" before accepting the top job at Camp Nou, while he continues to gain valuable coaching experience in the middle east.
"I'm convinced that Xavi will sign as Barcelona manager in the future and he is already getting prepared for that, starting his managerial career in Qatar, " Rivaldo said.
"I think he turned down Barca's offer because he's not yet ready to embrace such a task in an early phase of his new job as a manager. For now, he prefers to keep gaining experience and maturity as a coach.
"But while he didn't accept such responsibility now and will wait for the right moment, I'm sure he would be Barca's coach someday and hopefully with success.
"In the case of Koeman, it's different. He is an experienced manager with an international reputation and would have been a very good option.
"He is well known worldwide, has a good knowledge of the club and is used to big pressure like he will find in the Champions League and other competitions. But it didn't turn out to be the time for his comeback."