Pochettino said that he felt his team were worthy of three points in their last game against Arsenal, and was glad to respond to that draw with three away points in London.
"It was an excellent day," Pochettino told the club's official website.
"I thought we deserved more against Arsenal last week when we played very well and only got one point, so I think we redeemed that today.
"There were three great goals, a great performance and a great win. The three goals show the philosophy of how we want to play and seeing that as a manager makes me quite content and happy in the manner of how we scored the goals."
Southampton are ninth in the Premier League, eight points ahead of Aston Villa.