The Israeli prime minister was among those lobbying for Rich's pardon.
Holder declined to comment on whether his admitted failures in the pardon process reflected on his ability to vet vice-presidential candidates for Obama.
Holder referred calls to Lanny Davis, a former Clinton White House Special Counsel and friend of Holder's.
Davis told ABCNews.com that Holder's admissions should not be held against him.
"He stepped up to the line and said, 'you know what? If I had to do it all over again, I would have done it differently.' That shows that he learned a lesson," said Davis. "If anything, he is a better vetter having seen how in one moment in time you can miss asking additional questions."
Davis also said that Holder was distracted at the time because of security concerns over the pending inaugural ceremonies.
At the time, Republicans and Democrats were critical of Holder and the pardons.
"I am really disappointed in the inaction that characterized your treatment of this matter during the time that you were aware of it," Sen. John Kyl (R-AZ) told Holder at one of the hearings.
Congressman Paul Kanjorski (D-PA) said he agreed with Republicans that Holder's descriptions of what happened in the Rich case were "almost incredible."
"He neither recommended nor was he responsible for the pardon," said Davis.
"Whose responsibility was it? Was he the cause of the pardon or did someone else make the decision? Obviously it was somebody else named President Clinton."
Obama campaign spokesman Ben LaBolt said that Holder "did nothing inappropriate" in regard to the Rich pardon request, and defended the campaign's decision to select Holder to screen potential vice presidential candidates, stating that Holder is "a widely respected attorney who has spent the majority of his professional life in law enforcement and he is uniquely qualified to aid us in the search process."
While most of the attention at the time was focused on the Rich pardon, and the contributions Rich's ex-wife Denise made to the Clinton library and campaigns, there was also extensive criticism of the commuted sentences of two convicted members of the domestic terror group, the Weather Underground, Susan Rosenberg and Linda Sue Evans.