"From the very beginning I've had real concerns about the quality of the investigation," Daschle said in an interview with "Fox News Sunday."
"Given the fact that they already paid somebody else $5 million for the mistakes they must have made gives you some indication of the overall caliber and quality of the investigation."
The government paid $6 million to former Army scientist Steven Hatfill, who who accused authorities of unfairly targeting him in the anthrax case.
Daschle said the FBI has not briefed him about the matter in some time. Five people died and 17 others were sickened when anthrax-laced letters were sent to congressional offices, news organizations and post offices in the wake of the Sept. 11 terrorist attacks.
The case was thrust back into the spotlight this past week, as investigators prepared to charge government scientist Bruce Ivins in the case. However, Ivins died Tuesday in an apparent suicide.
"Unfortunately, it doesn't bring anything to closure," Daschle said. "This probably further complicates their ability to get to the facts."
However, former Homeland Security Adviser Tom Ridge defended the Bush administration's handling of the case in an interview on ABC's "This Week."
"I know that they were relentless, relentless, both domestically and overseas, both with the notion that it could have been a part of a broader terrorist network, but it could also have been the act of a deranged individual or two," Ridge said.