O'Neill resigned on Monday, reportedly because of a breakdown in his relationship with Villa's American owner Randy Lerner brought about by having to sell his best players while not being given cash in return for new signings.
But Krulak, Lerner's right-hand man at Villa Park and a former United States Marine Corps Commandant, insisted O'Neill had received full financial backing during his four years in charge of the Midlands club, who finished sixth in the table last season.
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"There is absolutely no question that Martin did a good job for Villa and I have said that over and over," Krulak told the Villa fansite VillaTalk.com on Tuesday.
"At the same time, I can promise everyone that he knew and understood the long-range plans for the club and bought into them.
"He knew full well about the need to bring wages in line with revenue - the same as every Premiership club.
"He was absolutely supported by the owner during his time with the club. All one needs to do is look at the money spent.
"The reality is that the wage-to-revenue issue was not addressed and Martin apparently was unwilling to help address it. He quit.
"No one person is bigger than our club - not me, not Randy, not Paul Faulkner (chief executive), not Martin.
"What is interesting is that, apparently, only three of those named understand that fact."
Villa begin the new season at home to West Ham on Saturday but Krulak stressed the board would refuse to rush into finding a replacement for former Celtic manager O'Neill.
"What I will say is that we recognise this is an important decision and one that needs to be done rather quickly but, equally important, in a manner that gets the right man.
"We do know how important this will be. No-one is thinking it will be easy."
Reserve coach Kevin MacDonald is currently in caretaker charge but among the candidates linked with succeeding O'Neill on a permanent basis is former England manager Sven-Goran Eriksson.
United States coach Bob Bradley, Ajax boss Martin Jol and Germany great Jurgen Klinsmann have also been linked with the job.
