Cantlie, in the five-and-half-minute-long recording, introduces himself as "the British citizen that was abandoned by his government and a long-term prisoner of the Islamic State".
In the video, he analyses Obama's speech made to mark the 13th anniversary of the 9/11 attacks, which the IS considered "expected", because he said that "America is good, while the Islamic State is bad".
Cantlie explained that Obama said that the IS would be defeated through "aircraft and a motley collection of fighters on the ground".
As in previous videos, Cantlie appears dressed in orange and is seated at a table with a black background. He announces that several more videos would be released.
It was Cantlie's third video in two weeks. The journalist was kidnapped in Syria by the IS in November 2012.
Since August, the extremist organisation has released videos of the beheading of three of their hostages: American journalists James Foley and Steve Sotloff, and British aid worker David Haines.