The Swiss banker has in his three years at St Mary's developed a reputation for ruthless decisions, including sacking former manager Nigel Adkins in January.
Cortese recognises his approach has been considered unconventional by some but, at the same time, he is not making any excuses.
"When I arrived in English football with a background as a Swiss banker, people looked at me like I was an extra-terrestrial," he said in the Daily Mail.
"The decisions appear ruthless but it was the right thing to do. At first I was hesitant, because football is so opinionated and everyone has a voice.
"It seems cold but I do everything in order to progress. I don't want to lose five matches in a row before I sack the manager - I do it before that happens."
Cortese added: "I want to do things differently and when that happens it creates suspicion, but I like to challenge the traditional views of English football.
"People automatically say, "You have to play like this in League One" or "This is the way to play in the Championship" and I would say, 'Why?'
"I am demanding, but I demand a lot from myself. I want to be an example to my staff and I don't tolerate anyone standing still."
Cortese has already this summer been busy, spending more than £20million on Victor Wanyama and Dejan Lovren, but he on Friday insisted the expenditure is all designed to improve Southampton.
"We try to create a fantastic working environment, whether it's in the offices or on a football pitch. It actually motivates people to work and to work even harder," he told Sky Sports News.