His name leaked to the press before Obama informed Feinstein, a California Democrat and incoming Senate Intelligence Committee chairman, who will oversee Panetta's nomination hearing.
"I have been contacted by both President-elect Obama and Vice President-elect Biden, and they have explained to me the reasons why they believe Leon Panetta is the best candidate for CIA Director," she said.
Feinstein complained Monday she had not been told about Panetta and expressed doubts he has the necessary experience.
There was no immediate comment from the Obama team, which has made no formal announcement of the CIA pick.
However, Vice President-elect Joe Biden told reporters at the Capitol that the Obama team made a "mistake" in not consulting with top Senate officials before deciding on Panetta.
Panetta is a congressional and White House veteran with a strong administrative background, but no intelligence-gathering experience.
Biden called Panetta a "strong figure" for the CIA who would "take it on a new path."
The Obama apology made headliness across the media world on Tuesday as some began to wonder what happened to No Drama Obama.
MSNBC's Chris Matthews had panelists discussing why both Obama and Biden apologize to Feinstein on Tuesday.
The Washington Post reported about Obama's fence-mending with Feinstein but said despite the California powerbroker's hurt feelings, Panetta was still expected to be confirmed for the post without a Senate challenge.