Rafa Benitez's side ended a run of four consecutive defeats with a fully-deserved 2-0 win over United last weekend - and the Argentina captain believes it is vital they build on the victory in order to gain momentum in the Barclays Premier League.
"We knew how important the game against United was and how much the fans enjoy it if we beat them," Mascherano told Liverpoolfc.tv.
"We are really happy for all of the supporters because they have been behind us all the time.
"But it was just three points and we have to keep going. We can't afford to be thinking about beating United and then, in this instance, go to Fulham and not play at the same level.
"If we want to fight for trophies we need to carry on and maintain the same level."
Liverpool head to Craven Cottage in fifth place in the table - just six points behind frontrunners Chelsea after 10 matches.
Mascherano insists the competitive nature of this season's division means a run of back-to-back victories can propel the Reds closer to the top.
He said: "In this league, everything is tight. If you can win four or five games consecutively, you can be at the top. That is the target for us now - we want to try and win some games in a row.
"We are confident in ourselves. We know if we are in good form and playing at a good level, we can play against any team in the world and win."
Last season, Yossi Benayoun struck a dramatic stoppage-time winner in SW6 to give the Reds a 1-0 victory - a moment Mascherano has fond memories of.
"It was a really difficult game for us there last season and we missed a lot of chances," he recalled.
"Yossi came on for the last 15 minutes and scored, which kept us going in the title race."
He added: "Fulham play good football and have players with quality. It will be a difficult game for us again, but we have to go to Craven Cottage with the same mentality we approached the United game with.
"We have to be focused on our next game. In this case it is Fulham, so we have to try to win there and carry on."