The Commissioner, who was in court to hear the guilty plea, spoke to members of Ms Everard’s family on Friday morning.
“My thoughts and those of everyone in the Met Police are with Sarah’s loved ones. It is not possible for any of us to begin imagining what they been going through”, she said.
“I was able to speak to them earlier today, and I say again how very sorry I am for their loss and for their pain and suffering.
“All of us in the Met are sickened, angered and devastated by this man’s crimes. They are dreadful. Everyone in policing feels betrayed.”
Couzens kidnapped Ms Everard on March 3 as she walked home through south London, driving her in a hired car to the Kent coast.
He transferred the 33-year-old marketing executive to his own vehicle, raping and murdering her at some point before her body was discovered in Kent woodland on March 10.
Couzens offered police a string of lies about the kidnapping, claiming he had been pressured into it by Eastern European gangsters and suggesting he had not been involved in the killing.
But he admitted kidnap and rape last month, and today confessed in court to the murder.
Paying tribute to Ms Everard, Dame Cressida said: “Sarah was a fantastic, talented young woman with her whole life ahead of her, and that has been snatched away.
“She was hugely loved and she will be sorely missed by so very many people.
“Ever since Sarah went missing, the sole priority of my investigation team, the search team, and hundreds of others in the Met and beyond was to find Sarah and to bring the person who had committed these terrible crimes to justice, as swiftly as we possibly could.
“In this, we are hugely indebted to Sarah’s family and to her friends and many members of the public who helped the investigation in every single way they could, not least by making appeals and giving us information.
“No words could adequately express the profound sadness and anger and regret that everyone in the Met, my police service, feels about what happened to Sarah.
“Today, as with every other day, our thoughts are with Sarah, with her family, and with her loved ones, and they always will be.”
The senior police officer did not name Couzens in her statement, and did not stop to answer questions from journalists outside the Old Bailey.
Jamie Klingler, one of the founders of the Reclaim These Streets movement which was established after Ms Everard’s death, today called on the government to do more to protect women’s safety.
“We have had enough and we want to see real change,” she said. “We want the government to make it a major issue.”
Scotland Yard’s lead investigator in the murder inquiry had to apologise to the court earlier in proceedings after a press release was issued by the Met, revealing that Ms Everard had been strangled.
“This was done before the material had even been considered by the reviewing lawyer, the court and the defence”, said prosecutor Tom Little QC, as the judge, Lord Justice Fulford, called the incident “undesirable”.
An investigation is also underway into how Couzens was suspected of indecent exposure three days before the kidnapping, but continue to work for the force and carry a firearm.
Lord Justice Fulford indicated he will consider a possible whole life term for Couzens when he passes sentence in September.