Revenue of $6.33 billion for its media networks unit slightly beat expectations and rose 8 percent from the previous year. But operating income for the segment fell 6 percent to $1.41 billion. The company said advertising and affiliate revenue grew, but was partially offset by "a decline in subscribers and unfavorable foreign currency translation impacts."
Operating income for the cable networks slid 5 percent to $1.2 billion "due to a decrease at ESPN," the company said. Still, Iger told CNBC that subscriber growth has picked up at ESPN since the quarter ended.
"We've actually seen an uptick recently in ESPN subs. We did reference, in candor, in the August call, that we had seen some sub erosion, and that in fact was the case. But the last few months, in particular, have been encouraging," he said.
Iger addressed the changing media landscape and the consumer shift from cable, saying that Disney's brands will help it to "contend successfully with ups and downs in the global marketplace."
"This is a company that is going to thrive in a new media world. Technology, in many ways, is propelling a lot more consumption of media, but it's propelling consumption of media that people want," Iger said.
Disney's parks and resorts unit, meanwhile, met analysts' expectations. Sales in the segment climbed 9 percent to $4.28 billion, while operating income rose 22 percent to $981 million.
The company also announced Tuesday that it would adapt its animated hit "Frozen" as a stage musical. The show is expected to start in 2018.
Before announcing fiscal first-quarter earnings, shares in Disney had seen a roughly 12 percent year-to-date slide — worse than rivals CBS, 21st Century Fox and Time Warner.
— CNBC's Everett Rosenfeld contributed to this report.