The former Liverpool man helped his side battle back from a goal down against their west London rivals, a result which sees them move level on points with his former club.
However, when asked if he thought a draw was a fair result, Murphy told Sky Sports: “I don’t think so, I thought we were good value. In fact, at one point we looked like we were going to win it.
“First-half we played some really good stuff and we felt a little bit aggrieved to go in a goal down.
“I’d like to see the stats because I thought possession-wise we were as good as them, if not better. We’ve played some great stuff at the Cottage and even though it’s only a draw I think that was one of the best performances of the season.”
The hosts’ equaliser came courtesy of in-form Clint Dempsey. The American now has 16 league goals to his name this season - his best return since moving to England - and Murphy was full of praise for the goalscorer.
He continued: “When you’ve got Clint in your team you’ve always got a chance, he does what he does best, he’s been on an unbelievable run of form.
“He keeps bailing us out and when the ball goes in the box he’s usually the first on the end of it and he’s got us out of trouble again.
“Overall I think we might have just edged it.”
Dempsey echoed his captain’s sentiments on the game, claiming they looked the better team as the game went on.
“The first 15 minutes of each half they were the better team but as the game went on we started to find space in the pockets, started passing the ball well, getting the ball out wide and getting the ball into the box, so we looked dangerous," he said.
The draw sees Fulham move up to ninth in the table and Murphy hopes they can emulate last season's achievements.
“Well it's difficult, I think last year we finished eighth so it’s going to be difficult to better that,” he added.
“We’ve got some tough fixtures to come at Everton and Liverpool but we’ll keep going, keep working hard, we’ve shown in recent weeks when we’ve had a few injuries that we’ve got strength in depth.”