"Obama clearly didn't know anything about him, who he was," the aide said. "Here's the guy who's going to run his [expletive] war, but he didn't seem very engaged. The boss was pretty disappointed."
McChrystal himself spoke openly about the time the president criticized him for speaking too bluntly about needing more troops last fall.
"I found that time painful," McChrystal said in the article. "I was selling an unsellable position."
After news of the comments stunned the political and military circles from D.C. to Afghanistan, McChrystal quickly issued an apology for his "bad judgment."
"I extend my sincerest apology for this profile. It was a mistake reflecting poor judgment and should never have happened," McChrystal said in a statement. "Throughout my career, I have lived by the principles of personal honor and professional integrity. What is reflected in this article falls far short of that standard."
In his apology, McChrystal said he had "enormous respect and admiration for President Obama and his national security team, and for the civilian leaders and troops fighting this war" and said he remains "committed to ensuring its successful outcome."
Duncan Boothby, a civilian press official in Afghanistan, resigned in the aftermath of the scandal.
Biden -- who one McChrystal adviser referred to as "Bite Me" -- was one of the few officials named in the story who did not comment, except to say Tuesdasy that he will have "plenty of time to talk about Afghanistan."
ABC News' Z. Byron Wolf and Jonathan Karl contributed to this report.