After a tight opening period, three goals in 11 second-half minutes from Adam Lallana, Rickie Lambert and Jay Rodriguez saw Southampton claim the three points.
The win came after the Saints had drawn 2-2 with high-flying Arsenal at home last time and Pochettino was delighted to secure the victory this time around.
He told Sky Sports: "It was an excellent day. The team deserved a lot more against Arsenal - the team played very well against Arsenal and had a very good performance but was only able to get one point.
"Today we redeemed that and today overall the team played very well, three great goals and a great performance and a great win as well."
He added: "I think overall in the first half, Fulham were playing quite deep and made it very difficult for us to actually open up the spaces.
"In the second half, once we scored the first goal, the game became a lot more simple, we were able to open up Fulham a lot more.
"The goals came in very quickly and we found a lot more spaces and we found ourselves a lot more comfortable in the second half."