The White House warned Friday that the government shutdown could undermine sanctions on Iran that have brought Tehran to the table to negotiate a halt to its nuclear weapons program.
Carney said that only 11 employees of the more than 100 who normally work in the office remained on the job, and cautioned the office would be "unable to sustain its core functions."
The White House said that with the shutdown, the office would be unable to issue new sanctions on those who provided financial assistance to Iran or terror groups.
"It illustrates the consequences that the Republican shutdown continues to have," Carney said.
When he was later asked about a quote by an anonymous administration official in The Wall Street Journal who declared the White House was "winning" the shutdown battle, Carney said "nobody wins" when Americans, like those who worked for the OFAC, weren't receiving paychecks.
He also credited the sanctions implemented by the office for bringing the U.S. and Iran "to the point where we are" in negotiations with Iran.
Last week, Obama spoke with new Iranian President Hassan Rouhani, the first discussion between Iranian and U.S. leaders in decades.
Rouhani has repeatedly expressed his desire to negotiate over the end of sanctions, which have crippled the Iranian economy.
On Thursday, Carney said the U.S. was "exploring the potential" of lifting sanctions if Iran ended its weapons program.
"We're going to test the theory," he said. "But it is because of the consensus and the seriousness of purpose and the commitment that the president has made to the idea that Iran cannot acquire a nuclear weapon that we are where we are."