Forwards Jay Rodriguez and Rickie Lambert were both on target before the break to ensure John Terry's goal for the visitors counted for nothing as Chelsea were beaten 2-1 at St Mary's.
The victory moved Saints up to 13th in the Premier League table and comes on the back of a similarly impressive triumph at home to Liverpool, and Pochettino is pleased with his players.
"It's not easy to get consecutive victories in our own stadium against hard teams like Chelsea and Liverpool," he told Sky Sports.
"We thoroughly deserved this win over Chelsea. We played very well so we are really happy with the performance and the result. Victories give us confidence in the job that we are doing.
"They were both quality goals. They are both strikers and strikers live off scoring goals. It's important that they have confidence going into the remaining games."
Southampton even made light of the loss of Artur Boruc at half-time when the goalkeeper was forced off due to dizziness and Pochettino made a point of praising his replacement Kelvin Davis.
He added: "I'd especially like to highlight the contributions of players who don't get much playing time, such as Kelvin. He came on for Boruc and did a really good job today.
"The work that happens behind closed doors isn't just something that managers say. It is something being done. It was a last-minute change and I'm really pleased."
Asked if Southampton can now push on for a top-half finish as the fear of relegation begins to fade, the Argentine coach said: "It is not important to look at the table at the moment. The most important thing is to prepare for the next match."