Galekovic expressed his disappointment about Sunday’s defeat to Brisbane Roar, declaring he felt 'gutted" by the result, at a media conference on Monday morning.
"I think it starts from the top and it goes all the way down and the main thing is football people need to make football decisions at this football club," he said.
"I think football people should just make those decisions - leave that for just football people.
"If there aren't any football people at this football club, maybe they've got to bring in people.
"One thing that needs to change is the culture of the football club," he said.
"Over the last few year we used to be the benchmark of the A-League.
"Every player wanted to come here and play for Adelaide United.
"I think that's changed."
Reds chairman Greg Griffin says the club would now undergo a review of the season, including meetings with all players, and proceed with finalising the new coach.
'The whole club feels the same disappointment as Eugene as to the end of our finals campaign," he said.
'The board, the football department and the coaching staff intended to meet this week to review the season gone. That will obviously be brought forward as Eugene has made some comments that we as a club have to address."
'The coaching selection panel is in place and we are expecting to be in a position to announce the new coach in the near future. The club respects the desire of the playing group that it knows as soon as possible who the new coach will be.
"It is a priority of the club to have this settled without delay, which was certainly an issue Eugene regarded as being important to him and the players."
'Eugene properly acknowledged the quality of the squad that has been assembled this year. Of that squad, 20 are contracted for next season.
"We appreciate that the stability we have created in the playing list now needs to be complemented by stability on the coaching side. We will work with the appointed experts to achieve what has to be done in this regard.
'The club will be scheduling meetings with all players so that any matters they wish to raise with the board and administration can be openly and frankly discussed.
'Whilst we are clearly disappointed with the forum Eugene has chosen to vent his concerns, it is a catalyst to have this open meeting to enable any other issues [from] players and staff to be raised and dealt with.
'This is the type of concern that some may have but for which there are perfectly reasonable answers. It is hoped that the process we start tomorrow will give all people associated with the club a better understanding of why certain decisions are made. If at the end of this we have a more transparent and accessible club, then the club will be a better place for it."