The Toffees are still hunting a replacement for Ronald Koeman nearly a month after the Dutchman was sacked.
On caretaker manager Unsworth, Barton blasted on talkSPORT: “He's a former defender and he can't set his team up to defend.
“They've shipped at least two goals in every game he's been in charge.
“The facts are that Unsworth is technically, tactically and strategically miles away.
“If Everton stay with him, they're going to get relegated, there's no doubt about it."
Barton added:“They need a proper manager who is going to come in quickly and he's going to change the culture into a winning one.
“What they need is a quick and decisive decision.
“David Unsworth is not the man for the job, it's nothing personal against him, he is not the man based on experience and strategy.
“Everton need to do their business and do it quickly, because they're turning into an embarrassment."