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Pochettino spoke before the season about challenging for Champions League qualification in the next couple of years and he believes that the start to the season can be maintained.
"We are not setting ourselves any limits," he said.
"We just have to keep on believing and the players believe fully in how we want them to play. We are now going to have to work harder because teams know more about us and will respect us a little more now."
With Osvaldo and Lambert netting their first goals since being partnered in attack and his defence again proving impenetrable Pochettino hailed the perfect day for his side.
"I think it is complete happiness for every manager is what happened today, a clean sheet and your two strikers getting on the scoresheet," he said.
"In the second half we were much better than the first half and over the 90 minutes we were the better team.
"We struggled a bit in the first half to understand the set-up of the game but after the break we corrected certain things and that allowed us to play much better in the second half."
The result leaves Palace with three points from their first six games since returning to the top flight. Full coverage of today's fixtures on the ITV Sport website here
Two goals early in the second half from Dani Osvaldo and Rickie Lambert secured the three points for Saints, who moved in to the top four of the Barclays Premier League with the win.
After a first half of very few opportunities it was Osvaldo who grabbed his first goal for the club moments after the restart with a Lambert free-kick two minutes later proving enough to kill off Palace.