With games against Everton and Liverpool to come, Murphy knows that it will be a tough test for his teammates.
"Last year we finished eighth so we will try and better that," he told the Fulham Chronicle.
"We know it's going to be difficult because we've got some tricky away games coming up.
"We'll keep going and have shown in recent weeks that we've got good strength in depth."
The Cottagers host next host Wigan Athletic in the league on Saturday.