"We're disappointed that the court failed to recognize that it has no jurisdiction to issue any order relating to these sanctions measures with the United States, which is doing its work on Iran to protect its own essential security interests", Pompeo said during a news conference at the State Department.
In a 29-page ruling, the judges said that USA sanctions could stop Iran importing humanitarian items and have "a serious detrimental impact on the health and lives of individuals on the territory of Iran".
President Trump pulled the US out of the Obama-era Iran nuclear deal in May and reimposed a number of sanctions against the Islamic Republic in August.
United States lawyers argued that the ICJ should not have jurisdiction and that Iran's assertions fall outside the bounds of the treaty.
Washington says that Iran's request is an attempt to misuse the court.
Though U.S. military officials have said protesters in the city unhappy over shortages may have been responsible, Pompeo said Iran was behind both the Basra incident and a mortar attack near the U.S. Embassy in Baghdad in early September.
In their ruling, the 15-strong panel of judges unanimously dismissed United States objections that the court had no jurisdiction.
During four days of hearings in late August, Iran's lawyers accused Washington of "strangling" its economy and its representative called the punitive measures "naked economic aggression".
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These attacks could involve Iranian-supplied missiles or not, depending on how strong or obvious Iran wants the connection to be. Last month s shooting in the Iranian city of Ahvaz killed 24 people and was claimed by the Islamic State militant group.
Iran said the sanctions violated the 1955 Treaty of Amity, Economic Relations, and Consular Rights between Iran and the USA, which grants the ICJ jurisdiction over disputes.
The court order issued on Wednesday was temporary, pending a resolution of Iran's full lawsuit against Washington at the ICJ, something that could take years.
But amid a broader push to assert US sovereignty in the global arena and after pulling out of the Iran nuclear deal this year, the administration determined that the court case made the treaty irrelevant.
It said U.S. sanctions must not hurt medicines and medical devices; foodstuffs and agricultural commodities; or parts, equipment and services necessary for civil aviation safety.
Iran's foreign minister, Mohammad Javad Zarif, praised the court ruling, saying on Twitter that it was "another failure for sanctions-addicted" USA and a "victory for rule of law".
The decision added to mounting tension between the US and Iran, which is the target of increasing USA economic sanctions. He also said that there are existing exemptions for humanitarians purposes in the sanctions regime. He added that it is imperative for the worldwide community "to collectively counter malign USA unilateralism".
US lawyers had told the court that the administration would "use its best endeavors" to look at concerns about humanitarian and aviation related issues caused by the sanctions.
FILE PHOTO: The International Court of Justice headquarters in The Hague, Netherlands August 27, 2018.