Saints travel to West Brom on Saturday looking to build on their impressive return to the Premier League last time out, and the Argentine coach is setting no limits to the club's ambitions.
"I think the sky is the limit," he said.
"We can't really set ourselves any limits, we have to think positive and be ambitious. We need to think that we need to win every single game and that every game is a final.
"We will go out looking to win on Saturday and the game after that and the game after that."
Southampton have added the likes of Dejan Lovren and Victor Wanyama to the squad and Pochettino is happy with the backing he has received from owner Nicola Cortese.
"I'm very happy with the support the owners have given me," he added.
"I'm very happy with the work that Nicola has done and the signings that have been made. Hopefully they will enable us to achieve the goals that we want to achieve for the club.
"I'm satisfied with the players we have in the squad - I'm happy how they have performed in pre-season.
"But if there is anyone out there who can make us better in general then they would be welcomed in to the squad.
He added: "We've very cautious with our work and there has always been a very good communication between me and Nicola when we have made decisions about buying players.
"It is clear there are some weeks left in the transfer window and we might be looking at a couple more players but again we will be keeping that in private."