Barra, who became CEO of the company in January, said in her letter that the problems were first brought to the attention of her team "a few weeks ago." She said she led a committee that acted immediately when informed about the problem.
GM has made numerous apologies about the delayed recall. GM North American President Alan Batey admitted in a statement last month: "The process employed to examine this phenomenon was not as robust as it should have been."
But this was Barra's first public statement on the matter.
In Tuesday's letter, Barra said that GM will launch an internal review "to give us an unvarnished report" about what happened.
"We will hold ourselves accountable and improve our processes so our customers do not experience this again," she said.
Why Mary Barra has never asked for a raise
She told employees she does not think GM's recently-improved reputation is being hurt by the recall of out-of-production vehicles that were made between 2003 and 2007, before the automaker's 2009 bankruptcy
"The vehicles we make today are the best in memory and I'm confident that they will do fine, on their own merits," Barra said. " And our company's reputation won't be determined by the recall itself, but by how we address the problem going forward."