Infantino announced that the plan would not proceed after three confederations rejected it, with UEFA going further and pledging to boycott FIFA competitions until the proposal was scrapped.
While UEFA welcomed the decision to drop the proposal, it believes Infantino has lost the trust of the football world through his actions.
"We cannot keep going on like this with secret schemes on fast track timescales, cooked up by faceless individuals and of dubious benefit to the game. We must identify those responsible and hold them to account," UEFA said.
"It is right that, in the coming days and weeks, UEFA will work with its associations and in close co-operation with other confederations to reflect on how this happened and devise a plan to make sure that it cannot occur again.
"That review should be thorough and fundamental. No option should be off the table. The current FIFA leadership has not only lost UEFA's confidence but also that of many other members of the football family."
UEFA's statement referenced an election speech from Infantino a decade ago, when he promised transparency.
UEFA added: "On both these promises, he has failed to deliver. The shabby, back room, opaque deal he hatched and tried to force through was anything but transparent."
UEFA's statement was followed by a similarly strongly worded response from North America, Central America and the Caribbean confederation CONCACAF.
The statement read: "A proposal of this magnitude does not reach that stage by accident. It is a symptom of leadership that has stopped putting football first."
Infantino was seeking approval to create a company, FIFA Forward Enterprise (FFE), to run commercial and operational aspects of its competitions, including the men's and women's World Cups.
Norwegian Football Federation president Lise Klaveness also issued a statement saying the "entire framework of international football co-operation was unnecessarily put at risk in pursuit of individual interests rather than the best interests of the game.
Infantino finally confirmed in the early hours of Saturday that the plan would not go ahead, with the Asian Football Confederation (AFC) also opposed.
Infantino appears intent to carry on despite the humiliation over FFE, admitting it had "created divisions" but adding: "my intent is to bring all interested parties back together in the coming days."
