Media speculation had mounted that the Argentine would quit after chief executive Nicola Cortese, the man credited with driving Southampton's renaissance as a force in English soccer, resigned on Wednesday.
Supporters feared an exodus of players loyal to Italian banker Cortese but Pochettino told a news conference he was "100 per cent committed" to his project.
"I have a professional responsibility to everyone at the club and to the fans," said the 41-year-old manager.
Pochettino said in May that he would leave the south-coast team if Cortese quit St Mary's but he has had a change of heart.
"It was a completely different situation eight months ago. I was speaking at the end of my first season," he explained.
"We are in the next process of this club ... I spoke to Nicola Cortese about this ... I am committed to this club, the staff, fans, players.
"It makes no sense to leave in the middle of this path. I want to express my complete gratitude to Nicola for bringing me and my family to the club."
Pochettino said the former chief executive had backed his decision.
"Nicola agrees with my decision to stay," said the Argentine. "He asked me for only one thing and that was to try to win on Saturday against Sunderland."
Owner Katharina Liebherr has taken on the role of non-executive chairman and a search has begun for a new chief executive at the club that was in the third tier of English football in 2010.
Pochettino said he had met briefly with Liebherr who had stressed her faith in the manager.
"I spoke to her for five minutes and she transmitted to me her full trust," he added.
"There was not time to speak to her about the future. It was a quick hello and goodbye."
Pochettino said it was only the second time he had met Liebherr who inherited Southampton when her Swiss father Markus, who bought the club for around £14 million in 2009, died a year later.
The manager said he was unaware of any intention by Liebherr, who according to media reports is worth three billion pounds, to sell a club that is valued at around 100 million pounds.
"She said she wants the club to be stable and for this to not affect the club and to look forward to the future," said Pochettino.
The former Espanyol coach also moved to snuff out rumours that rival clubs were circling, ready to take advantage of the turmoil at Southampton by snapping up some of their highly-prized players like left back Luke Shaw.
"I want to make this clear...my belief has not changed from a week ago," said Pochettino. "No players that I want at this club will be sold."
Pochettino added that he would review his position at the end of the season.
Southampton are ninth in the league, 12 points behind Liverpool - who occupy the fourth spot that will earn a berth in the Champions League preliminary round next season - and 12 points clear of the relegation zone.