The Toffees sit 12th in the Premier League, 19 points worse off than at this stage last season, and Nevin believes their strength in key positions means they may well be staring down the barrel come May.
"Everyone knows there's no such thing as too good to go down," he said.
"Players like Ross Barkley, Romelu Lukaku and Leighton Baines are undoubtedly international class, and that's the sort of thing that gets you relegated.
"You look at teams like Crystal Palace, West Brom and Sunderland, and they're chock-full of the kind of useless spanners who are perfectly cut out for finishing 16th. They're more than bad enough to stay up. Everton are far superior, and that definitely counts against them."
But manager Roberto Martinez has rubbished suggestions that his team might not have enough mediocrity to finish the season strongly.
"We have dead wood in every position," the arguably-balding Spanish tactician insisted. "Gareth Barry is clearly past it, Kevin Mirallas can't wait to leave, and if Steven Naismith is the answer then it must have been a bloody stupid question.
"Players like these will drag us into the top half with their blend of one-paced clogging and half-arsed bursts of quality. Of course we're not too good to stay up."
The curse of being too good to stay up has struck many times in the past, with Middlesbrough in 1997 and West Ham in 2003 being the most notorious examples.
Abroad, Villareal's 2011/12 season began in the Champions League and ended inevitably in relegation, while it was universally agreed that Juventus were far too good to stay up after winning Serie A in 2006.
SEE ALSO Too good to go down? Beware Dortmund, the teams that weren't
