A White House photo shows Mrs Salahi meeting Mr Obama
The US Secret Service chief says three agents have been placed on leave after a socialite couple gatecrashed the Obamas' debut state dinner.
Mark Sullivan told a congressional hearing that mistakes had been made, but said he was confident US President Barack Obama had not been at risk.
He described the incident at the White House event, during which the couple met the president, as an "aberration".
The White House said it would enforce new rules to monitor official events.
A senior official said White House staff would work alongside Secret Service agents on such occasions from now on.
Virginia socialite couple Michaele and Tareq Salahi were allowed to attend the state dinner, held for the visiting Indian prime minister, despite not having invitations.
'Night of horror'
Mr Sullivan, director of the Secret Service, was the only official to testify before the House Homeland Security Committee on Thursday.
Secret Service chief Mark Sullivan said mistakes had been made
The Salahis were invited but declined to appear. The White House also refused to send its social secretary, Desiree Rogers, to the hearing.
Acknowledging that proper procedures were not followed, Mr Sullivan told the panel: "In our judgment, a mistake was made. In our line of work, we cannot afford even one mistake."
He said three agents, identified by his office as being from the Uniformed Services Division, had been placed on administrative leave.
Committee chairman Bennie Thompson said the country was lucky the incident had not led to a "night of horror".
"This hearing is not about crashing a party at the White House. Nor is it about wannabe celebrities," he said.
"There were undeniable planning and execution failures of the entire Secret Service apparatus."
In a statement on Wednesday, the White House appeared to be taking some of the blame for the security breach.
"It is clear that the White House did not do everything we could have done to assist the United States Secret Service in ensuring that only invited guests enter the complex," White House Deputy Chief of Staff Jim Messina said.
The incident, which is said to have angered President Obama, has drawn a rare public apology from the Secret Service which said it was "concerned and embarrassed".
A Secret Service investigation found the couple should not have been allowed in.
Tareq and Michaele Salahi went through security checkpoints at the dinner hosted by Mr Obama and later posted photos of themselves on Facebook.
According to their publicist, the Salahis have already provided the House Homeland Security Committee with statements and e-mails between themselves and a Pentagon official whom they pressed for tickets and believe there is nothing further they can do to assist.