Everton lost away to promoted Bournemouth 4-1 in the EFL Cup in the third round of the competition on Tuesday night.
They are currently placed 16th in the Premier League table, despite still boasting the third-best defence in the top flight.
Murphy pointed to recent winners of the EFL Cup, where Swansea City in 2014 were the last team that won the competition and finished outside the top four of the Premier League.
Given that scenario, Murphy feels that there was no chance that the Toffees could have clinched the EFL Cup in the current campaign.
While not excusing their collapse at Dean Court, Murphy noted that the biggest priority for Frank Lampard’s side will be survival in the Premier League.
“The EFL Cup, if you look at it, I can’t remember the last time a team outside the top four won it”, Murphy said on talkSPORT.
“[Manchester] City have dominated for years, Liverpool won it last year.
“Swansea, yes, that was quite a while ago, wasn’t it?
“Everton aren’t winning it [the EFL Cup].
“They’re not winning it this season but they should be more competitive.
“Staying in the Premier League is the priority.”
Everton face Bournemouth at the same venue in the Premier League on Saturday in their final fixture before the World Cup break.
