The Argentinian's arrival at St Mary's came in controversial circumstances last month, when he surprisingly replaced the popular Nigel Adkins at the helm.
However, talk of a fan backlash never came to fruition and Saints have begun impressively under his guidance, including last weekend's 3-1 defeat of reigning champions Manchester City.
"I said three weeks ago, it's never nice when they sack one of my colleagues," Pochettino said.
"I got an offer from Southampton and I said yes. I had other offers from other teams but I chose Southampton.
"For me there is no controversy, it's just to work and to work from day one and I will carry on working in the project."