Speculation was rife that Cortese’s departure would spark a mass exodus with manager Mauricio Pochettino - a close friend of Cortese - reported to be considering his position.
But the Argentinian boss has since stated he will remain at St Mary’s and maintained that none of the club’s star players would be leaving in the January transfer window.
Saints chairman Katharina Liebherr told the club's official website: "The past week has been a period of transition for the club. I wanted to address you directly to clearly set out my position and expectations for the immediate future.
"After the developments of last week, my priority now is to bring some stability and calm to the workings of the club; perhaps a few smiles too."
"Having inherited Southampton Football Club following my father's untimely passing, I am delighted and proud of the exhilarating period of success that the team and the staff has enjoyed these past few years, buoyed by the unstinting support of the fans," she continued.
"I am absolutely committed to ensuring that the club continues this success. I have met our manager Mauricio Pochettino and have given him my complete support to build on the good work that has already been achieved.
"We have also said that we have no plans to sell any of the squad during the January transfer window. Yesterday (Tuesday) I met the rest of the staff and gave them the same message of support.
"Off the pitch, my priority is to establish the proper running of the club at the top. I also have a strong team of advisers around me as we plan the way forwards. As soon as we have more news to share, we will do so."
- Sports & Recreation
- Mauricio Pochettino
- Southampton Football Club