Mingueza, 22, was promoted to the first team by Koeman and handed his full debut by the Dutchman, but believes a change of manager was needed at Camp Nou as results deteriorated.
"We weren't good individually or collectively. When the dynamic is not good, everyone does what they can, but we didn't believe in what we wanted, either. I am sure that things get better now.
"The dressing room needed a change. There wasn't the atmosphere that we needed. People weren't happy. And when things aren't good and don't go well, you need a change."
Xavi, who made 767 appearances for Barca as a player before leaving in 2015, has replaced Koeman after leaving Al Sadd, who he led to seven trophies in just over two years in charge in Qatar.
"He will be very good for us," Mingueza added. "The ideas that he has come in with are very good. He has got off to a good start with the dressing room. People believe in what he says and that's very important."
Xavi's return has lifted the mood around the club and drawn parallels with the appointment of Pep Guardiola in 2008. Defender Eric Garcia, who played under Guardiola at Manchester City, can see similarities between the two coaches.
"Right now, [Xavi] is the right person for the job. He is a legend who knows the club well and he will help us all a lot. He has been through these types of situations before and is a great coach."
One of the first things Xavi has done is re-introduce a series of rules that have gradually been discarded since Luis Enrique left the club in 2016.
Sources have told ESPN that the former Spain international has re-introduced a fines system, wants players at the training ground 90 minutes before training and, among other things, will monitor their activities away from football.
"It's all completely normal," Garcia said of the rules. "I had them when I was at City and you always need a little bit of discipline."
Xavi will take charge of his first game against Espanyol at Camp Nou this weekend before a home fixture against Benfica in the Champions League on Nov. 23. Barca can book their place in the knockout rounds with a match to spare if they beat the Portuguese side.