Boris Johnson paid tribute to Stratton in a press conference as he said she was “outstanding” in her role and did an “extraordinary job” with Cop26 after her resignation.
A heartbroken Stratton broke down in tears as she apologised for joking about the strict rules amid the coronavirus pandemic last Christmas.
She said in a statement: “My remarks seemed to make light of the rules everyone. That was never my intention.”
“I will regret those remarks for the rest of my days and offer my profound apologies to all of you for them.”
She added: “Working in government is an immense privilege. I tried to do right by you all, to behave with civility and decency and up to the high standards you expect of Number 10.”
Ms Stratton said she understood the “anger and frustration” people feel.
She added: “To all of you who lost loved ones, who endured intolerable loneliness and who struggled with your businesses, I am truly sorry.”
The former ITV journalist, who served as the spokesperson for the Cop26 climate summit, was filmed discussing a Christmas gathering during rehearsals for a proposed daily televised Downing Street press briefing.
During the mock press conference, one aide was heard saying: “It wasn’t a party, it was cheese and wine.”
“Is cheese and wine all right? It was a business meeting,” Ms Stratton replied, to laughter in the room.
Ms Stratton then noted “this is recorded”. She added: “This fictional party was a business meeting… and it was not socially distanced.”
The comments provoked a furious response, with Boris Johnson later forced to “unreservedly” apologise for her remarks.
But he insisted he had been repeatedly assured “there was no party and that no Covid rules were broken”.
Mr Johnson has ordered an inquiry into reports of an illegal Christmas party.
He said he had asked Cabinet Secretary Simon Case “to establish all the facts and to report back as soon as possible”.
“It goes without saying that if those rules were broken then there will be disciplinary action for all those involved,” he added.