It is an interesting question, so I figured checking The Dismantling of Yugoslavia: A Study in Inhumanitarian Intervention (and a Western Liberal-Left Intellectual and Moral Collapse) for a possible answer might be enligthening. I will just run through and cut comments focused on the US and EC (as the EU was namned then) acting in Yugoslavia around 1990 and then see what comes out of it.

Monthly Review

The collapse of the Soviet bloc a decade later deprived Yugoslavia of Western support for the unified state. As the last U.S. ambassador to Yugoslavia purportedly instructed Belgrade upon his arrival in April 1989: "Yugoslavia no longer enjoyed the geopolitical importance that the United States had given it during the Cold War.

Monthly Review

Had Western powers supported the federal state, Yugoslavia might have held together--but they did not. Instead they not only encouraged Slovenia, Croatia, and later Bosnia-Herzegovina to secede, they also insisted that the federal state not use force to prevent it. Diana Johnstone recounts a January 1991 meeting in Belgrade between the U.S. ambassador and Borisav Jovic, a Serb then serving on Yugoslavia's collective State Presidency. "[T]he United States would not accept any use of force to disarm the paramilitaries," Jovic was told. "Only `peaceful' means were acceptable to Washington. The Yugoslav army was prohibited by the United States from using force to preserve the Federation, which meant that it could not prevent the Federation from being dismembered by force"12--a remarkable injunction against a sovereign state. Similar warnings were communicated by the EC as well.

Monthly Review

One way this was accomplished was by the EC's September 1991 appointment of an Arbitration Commission--the Badinter Commission--to assess legal aspects of the contests over Yugoslavia. This body's work provided a "pseudo-legal gloss to the [EC's] opportunistic consent to the destruction of Yugoslavia demanded by Germany," Diana Johnstone writes.14 On each of the major issues contested by the Serbian republic, the commission ruled against Serbia. Yugoslavia was "in the process of dissolution," the commission's notorious Opinion No. 1 stated when published on December 7, 1991. Similarly, Opinion No. 2 held that "the Serbian population in Croatia and Bosnia-Herzegovina...[does not] have the right to self-determination," though it "is entitled to all the rights concerned to minorities and ethnic groups under international law...." And Opinion No. 3 declared that "the [former] internal boundaries between Croatia and Serbia and between Bosnia-Herzegovina and Serbia...[have] become frontiers protected by international law."15 Remarkably, the commission recognized the right of republics to secede from the former Yugoslavia, and thus affixed the right of self-determination to Yugoslavia's former administrative units; but the commission detached the right of self-determination from Yugoslavia's peoples, and thus denied comparable rights to the new minorities now stranded within the breakaway republics.

Monthly Review

Germany in particular encouraged Slovenia and Croatia to secede, which they did on June 25, 1991; formal recognition was granted on December 23, one year to the day after 94.5 percent of Slovenes had voted in a referendum in favor of independence. EC recognition followed on January 15, 1992, as did U.S. recognition in early April, when Washington recognized Slovenia, Croatia, and Bosnia-Herzegovina all at once.

The picture I get is that the formal recognition played only a minor part in the breakup and that in the important part of forbidding the federal government to use state violence against the militias, the EC and US cooperated.

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