Alex Iwobi struck twice for the visitors, but the Hammers won through goals from Carlos Soler, Tomas Soucek and Lucas Paqueta.
Potter said afterwards: "It feels great. It's a big three points for us. It was hard-fought in a tough game, a London derby. Fulham started the game as a better team. We had some trouble trying to put pressure on them, but we changed that in the middle of the first half and were more aggressive. That helped us to put some pressure on them.
"We were disappointed to concede the goal early in the second half, but credit to the players, they stuck at it and stuck together.
"The start point is the foundation of togetherness and the foundation of a team. We were far from perfect. But in terms of application of the players and how they fought and suffered, they were really, really, good. We have to look at the context of what happened and it's been a tough week for the players and we have players missing, especially in the forward areas. But nevertheless, the team spirt, the team effort and willingness to try were fantastic."