Blackmun offered no details on what disciplinary action may be coming, but he made no effort to hide his frustration with the matter.
"They let down our athletes," Blackmun said. "They let down Americans."
Lochte originally described the Aug. 14 incident as an armed robbery, before the story unraveled.
In an interview with NBC that aired Saturday, Lochte backtracked and said he "overexaggerated" the story.
"That's why I'm taking full responsibility for it, because I overexaggerated the story," Lochte said. "If I had never done that, we wouldn't be in this mess."
Police said Lochte, Jimmy Feigen, Jack Conger and Gunnar Bentzvandalized a bathroom after a night of partying. Armed guards confronted the swimmers and asked them to pay for the damage.
"It's how you want to make it look like," Lochte told NBC's Matt Lauer. "Whether you call it a robbery or whether you call it extortion or us just paying for the damages, we don't know. All we know is that there was a gun pointed in our direction and we were demanded to give money."
Lochte said he originally spoke to NBC's Billy Bush the day after the incident while still under the influence of alcohol.
Lochte returned to the United States during the week. Feigen followed Friday night, but only after reaching a deal with a judge to make a $10,800 payment. The trip home for Bentz and Conger was a little more eventful.
They boarded a plane Wednesday night to leave Rio, but authorities removed the pair from the jet. Police were not satisfied with their account of the robbery-that-wasn't and wanted more information. Bentz and Conger talked with authorities Thursday and were whisked through airport security and got on a plane that night. They were greeted back home with yard signs that said "Go Jack" and "Welcome Home."
Blackmun said Lochte's story harmed Brazil in how the storyline took a great deal of attention off the Rio Games themselves.
Lochte said he regretted how the incident had tarnished Rio and the final week of the Olympics. He also gave an interview to Globo, Brazil's main broadcaster, on Saturday to apologize for his actions.
"Brazil doesn't deserve that," Lochte said to Globo. "I am sorry that my immaturity caused all this ruckus."
Lochte has said he hopes to compete at the Tokyo Games in 2020.
The Associated Press contributed to this report.