The club’s manager also moved to calm fears of a reported player “exodus” this month, saying no one who he wants to keep will be allowed to leave during the transfer window.
Pochettino was speaking for the first time since Cortese’s shock exit on Wednesday night and just moments after meeting owner Katharina Liebherr at St Mary’s.
He revealed he had received the full support of Liebherr and was “100 per cent committed” to Saints, although he gave mixed messages about how long for.
“It is clear that there is a loyalty and a commitment to this club and to the staff, to the people that run this club, to the supporters of this club,” said the 41-year-old, whose contract runs until the end of next season.
“My contract is with Southampton, it’s with a company, and I intend see my contract with this company. It would not be the right moment to actually leave this club right now.”
At another point, he added: “What is clear is when I signed for Nicola I signed for two years. We signed together a number of players, and I am 100 per cent committed to those players, and 100 per cent committed to the project, to the two years of my contract.”
However, Pochettino – who admitted yesterday he contemplated quitting due to Cortese’s departure – later said he would review his status as manager at the end of the season.
“I am fully 100 per cent decided on staying here at this club until the end of the season and taking this club as high as it can,” he said.
“First, it’s only normal that we finish the season, then we’ll see next season what happens.
“It’s clear that at the end of the season we will assess the situation at the club and then we will decide whether I am up to staying here another season.”
Last summer, when Cortese’s future was under threat, Pochettino had aligned himself closely with the Italian, saying he would leave if he departed.
However, he justified his decision not to follow him out of the door this time, as circumstances had changed.
“It is clear that when I came in in the middle of last season Nicola wanted me to be here for those four months to ensure the club stayed in the Premier League, and from then on a new project started, so that’s a different situation to what I said before,” he said.
“It would make no sense for me to leave this club in the middle of the season – no one would understand it. I am sure Nicola would not understand that.”
Pochettino, who added Cortese agreed with his decision to stay, only spoke to Liebherr for about five minutes yesterday and confirmed they had not discussed issues such as the transfer market.
However, he laid down a marker that he does not expect anyone to be sold who he wishes to keep.
“I’m sure that the club will designate a person to receive any potential offers, to speak to any potential buyers, and to deal with all these potential offers.
“But I want to make something very clear; no one is for sale at Southampton, no one. My belief has not changed from one week ago. No player that I don’t want to leave will leave this club.”
Perhaps the biggest concern among supporters is the future of teenage left-back Luke Shaw, with reports suggesting he wants to leave and that clubs such as Chelsea, Manchester City and Liverpool are now preparing moves for him.
Pochettino put the ball in Liebherr’s court over that issue.
“That is not a question I can answer,” he said. “Luke Shaw has a contract and that is a question for the new chairman. I am not aware of bids for him.”
Rickie Lambert has also this week been linked with a move to West Ham, with suggestions that Cortese was involved in negotiations over a £7m deal in the hours leading up to his departure.
“I have no news on that,” said Pochettino.
Asked what Lambert wants to do, the Saints boss said: “I have not spoken with him yet, so I do not know.”
Pochettino said he had received no indication from any player that they wished to leave.