Last Updated Aug 20, 2014 12:22 PM EDT
In the video, an ISIS executioner who speaks with a British accent threatens to kill a second American journalist, Steven Sotloff, if the U.S. military continues airstrikes against the Sunni Muslim extremists in northern Iraq.
CBS News contributor and former deputy director of the CIA Mike Morell explained on "CBS This Morning" that the beheading is a very significant moment.
"The definition of terrorism is political violence, violence for political effect," Morell said. "We should mark the date down, because this is ISIS' first terrorist attack against the United States."
ISIS, Morell said, is very clearly "trying to intimidate the U.S. into backing off" from the policy of airstrikes in Iraq.
"I think our response should be, and I think our response will be, to not do that," said Morell, who used to be in charge of preparing President Obama's daily intelligence briefings.
He said, if anything, the U.S. military should "pick up the pace" in its fight against ISIS, and in helping Iraqis reclaim territory from the militants who now pose a clear and direct threat to the United States.
British officials have said as many as 400 nationals are believed to have traveled to Syria and Iraq to join ISIS on the battle field.
Dozens of Americans have done the same, and the fact that one of those Westerners appears to have killed Foley highlights the risk of radicalized jihadists with Western passports, which Morell deemed the "main danger that ISIS now poses to the United States -- that is the number-one thing we need to worry about."
As for the threat from ISIS to kill Sotloff, Morell is adamant that it must not deter the American government's policy on stopping the terror group's advance.
"We need to keep moving forward with our policy," he told "CBS This Morning" co-anchor Norah O'Donnell. "I would suspect that ISIS may assassinate him, but we need to keep moving forward. We cannot let something like this stop us."