Despite guiding the Saints to back-to-back promotions and keeping them clear of the Barclays Premier League relegation zone following a battling 2-2 draw at Chelsea, Adkins was unceremoniously axed and replaced by Argentinian Pochettino as the south-coast club sought a change of direction.
Southampton's executive chairman Nicola Cortese has defended the controversial sacking of Adkins, describing the timing as "perfect".
Nevertheless, the club came in for criticism after Adkins' name and photo were not included in the matchday programme for last Monday night's goalless draw with Everton at St Mary's.
Former Espanyol coach Pochettino used the break in domestic action to take the group away to a short training camp in Spain which he believes has helped the players and new staff to bond.
While Pochettino is determined to stamp his own mark on the team, which heads to Manchester United on Wednesday night, the Argentinian remains conscious of what the squad had achieved before his arrival.
"We have our own work ethic and our own philosophy as to where we want to take the club," he said. "We have goals and ambition, we want to work for the team to achieve those goals."
"However, that does not mean we want to be anything contrary to what was being done before, it is not about that.
"It is more about our philosophy, how we want to take the team forward and how we want to achieve those goals."
With defender Jose Fonte still missing through injury, new signing Vegard Forren could make his debut at Old Trafford after joining from Norwegian side Molde.
Pochettino hopes the 24-year-old, who has not played a competitive match since December, will settle quickly into the hustle-and-bustle of the English Premier League.
"We are very pleased Forren has decided to come here. He is a player who is going to cover certain necessities of the squad," the Southampton manager said.
"The most important aspect now is he adapts well to the team, is up to speed and will be able to compete with us."
One target who eluded the Saints, however, was Philippe Coutinho as the Inter Milan midfielder headed to Liverpool instead.
Pochettino worked with the 20-year-old on loan at Espanyol last season.
"I am not frustrated about not being able to sign him. I knew there was a small chance he would come here, but overall I have not had much time to consider new signings," he said.
"I am very happy with the squad which is available to me.
"We all know who Coutinho is, and that he is a quality player. However, there are other factors when we want to sign a player."
The Saints head to Old Trafford four points clear of the relegation zone, and travel to struggling Wigan on Saturday before hosting Premier League champions Manchester City on February 9.
Pochettino remains confident his current group of players have what it takes to stay clear of being dragged into a dogfight for survival.
"I am happy with the quality of the squad and am confident we can do well in the league," he said.