Two second-half goals in as many minutes from Pablo Daniel Osvaldo and Rickie Lambert secured the hosts' first home league win of the campaign, moving them up to fourth.
The triumph comes on the heels of a 1-0 victory at Liverpool and a 2-0 League Cup success against Bristol City, wih Pochettino's men having kept four clean sheets in a row.
But the 41-year-old insisted that his men need to remain calm as they look to continue their promising early-season form.
"Experience tells us that you need to be calm, need to keep your feet on the ground, more now you have to even work harder because teams will respect us more, they will actually know who we are," he told BBC Solent Sport.
"So we have to keep our feet on the ground, work harder, and that's actually hard for these players because they are already working quite a bit so to actually make them work harder is going to be interesting.
"I think belief is key, I believe in my players, they believe in how they are playing and how the team is playing and it's going to be a very long season and it will be very hard but overall my players are going to believe how we want them to play and we just need to keep on working hard."
Pochettino's men host Swansea City at home next Sunday as they look to continue their winning streak.
