The Saints boss warned his players that more will be expected of them after their start to the campaign, while Michael Laudrup indicated his side didn't deserve to lose
Saints kept up their impressive start to the season with a 2-0 win over Swansea on Sunday, leaving them among the Champions League places, with the Argentine warning his players that their form is sure to bring about higher expectations.
He told reporters through an interpreter: "We need to understand that the higher we are in the table the more pressure our players are going to have, and they need to go through that learning process where a lot more is going to be expected of them.
"That's what we're going to work on in the international break."
But the 41-year-old stressed that he is enjoying the demands that comes with those higher expectations, while challenging his players to work even harder in the future.
"I always look forward to this kind of pressure during my career," he continued. "It's what I thrive on and what I relish.
"I'm fully aware that what we've done until now doesn't count for anything if we don't keep up this run. We just need to work harder becuase the expectation on us is going to be a lot bigger.
"That just means the players need to be a lot more self-demanding, they need to be very ambitious, and learn how to withstand this great expectation that's going to be placed on them."
The former Espanyol manager then moved to praise Adam Lallana, who scored Saints opening goal, and goalkeeper Artur Boruc, who made a number of fine saves to keep his team ahead.
"I'm very happy for Adam, he's great guy, he's a great professional, and he feels passionate about Southampton," Pochettino added.
"It's not my decision in the end [whether he gets an England call-up] but if he keeps on preforming as he has done today he'll be very close to getting that call-up to the national side.
"Boruc was incredible. We were able to keep another clean sheet which is a massive positive for us. It shows he has our full trust to be our number one keeper."
Swans manager Michael Laudrup, meanwhile, bemoaned his side's failure to take their chances in a game in which he believes they dominated for the most part.
"It is true that Southampton for the first 20 minutes were the better team," he said. "After the goal I think we dominated the whole game. We created three chances on the keeper plus we hit the post in the first half. In the second half we dominated from first to last minutes but maybe [didn't] create the same number of chances."
In more general terms, the Dane urged his side to be more direct in the final third of the pitch, highlighting the fact they have only been awarded one penalty since he took charge.
"It's incredible that with the way we play, offensive football and all that, I've been here now for 15 months and we've played 45 league games - not a penalty. I think we've played 61 games since I've been here - one penalty in the [Capital One Cup] final.
"Maybe in the last third sometimes we could go in there, just get one against one and we will get them.
"Sometimes we want to make that nice pass and combination - it's not becuase I thought there was a penalty today, just in general - I will never say that someone has to dive in there but it's strange that the way we play we haven't got a penalty."