"Liverpool fans, of which I'm one, can be forgiven for seeing a glass half-empty at times because we've seen some promising title challenges fade since the last success in 1990."
Liverpool take on Manchester City, the title favourites before the off, on Thursday in the biggest game of the season so far.
Murphy said: "It's right to still keep things in perspective because it's possible City will only be four points behind at the end of the week if they beat Southampton today and then Liverpool later in the week.
"But if Liverpool do go to City and win, it becomes real. The players will have to stay humble at all times but three points at the Etihad will convince even the most pessimistic supporter that the championship is coming back to Anfield.
Liverpool transfer news: Jurgen Klopp spend £75million on Viril van Dijk last January (Image: GETTY)
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"And it will take a hell of a side to stop them at the moment."
Liverpool have won all eight games they have played in December but their five-star showing over Arsenal was the highlight.
Jurgen Klopp's side went behind early on through Ainsley Maitland-Niles before Roberto Firmino's hat-trick and one each from Sadio Mane and Mo Salah sealed a stunning comeback.
"You can talk tactics all you like — Mo Salah playing up top, Roberto Firmino in behind, Liverpool's improvement defensively. But it wasn't tactics that helped them destroy Arsenal last night, it was a super quality and confidence allied to collective energy and appetite," Murphy said.
"I found it remarkable because to put in a performance of that hunger in late December takes enormous physical dedication on and off the pitch all season, particularly when you've got a fixture list like Liverpool.
"It was Liverpool's 27th game of the season, their eighth this month, and yet they were still at it to a man. They steamrollered Arsenal."