Koeman was announced as Quique Setien's successor on Wednesday, signing a two-year deal at Camp Nou, where he spent six hugely successful years as a player under Johan Cruyff.
But Deulofeu, who played under Koeman at Everton in the 2016-17 Premier League season, does not appear to think much of his old manager's chances.
"I can tell you about Koeman from my personal experience, and I have very little to tell you about Koeman," the Watford winger said on Cataluna Radio.
"He provided me absolutely nothing. I wasn't happy, I asked to leave and I went to Milan.
"We'll see how he does at Camp Nou."
Deulofeu, a product of Barca's youth academy, was sold to Everton in 2015 after spending the previous seasons on loan with the Toffees and then Sevilla.
He was signed back by Barca in 2017 but failed to make an impact under Ernesto Valverde before joining Watford.
Despite his past allegiance to the club, the 26-year-old does not appear concerned by the institutional crisis at Barca, who saw Eric Abidal leave as first-team technical secretary the day after Setien was dismissed and who are facing a battle to convince captain Lionel Messi to stay.
"The truth is that Barcelona's [situation] does not bother me," he said. "In fact, right now, I don't care."
Deulofeu thinks it will be "years" before Barca are able to rival the very best sides in Europe again and says they have paid the price for not trusting youth.
"At Barcelona, they have not had patience with La Masia for years," he added. "If you give [the youngsters] time, they learn the style of the first team.
"There are players, many of us have come from there, but not [been given] patience. Now, there will be changes, but they are years behind."