The win was the first Adkins has masterminded as Royals manager, and only the second time the men from Berkshire have tasted victory away from the Madejski all season.
But Adkins was pleased with how his side performed despite already being relegated from the top flight.
"We have to target progression in the final games of the season," he told Sky Sports.
"The reality is there has been a change at the club, it is a shame where we are, but we have to keep looking forward.
"Credit to the players. We played some really good football. To come away from home, and score four goals is very exciting for the supporters."
However, Fulham were allowed back into the encounter very easily, and Adkins knows that they have to cut out the defensive errors if they are to bounce straight back up.
"We are disappointed with the goals we have conceded, and the manner in which we let Fulham in," he added.
"There could have been a few penalty decisions that would have gone our way, but we are happy to come out on the right side, and from here we will move on and try and encourage further progression."