The former Arsenal and Everton defender says his old club are in a relegation battle.
The Blues are currently 14th in the table, just six points above QPR and Burnley in 18th and 19th place respectively, leaving many Everton fans fearing relegation at the end of the season.
In fact, even the Everton squad are concerned about the possibility of dropping down to the Championship, with captain Phil Jagielka admitting after the 2-0 loss to Stoke on Wednesday evening that his team are in a dogfight, according to the Mirror.
Keown is backing his former club to avoid the drop this season, but admits that their form is worrying and they will have to scrap for points in order to prevent a tumble into the second tier.
“I don’t think they will go down, but you can’t say they are too good to go down,” he answered to a fan question on the subject.
“Their run of form is very concerning. Martinez is obviously a very creative manager and loves to play an attacking team, but at the moment they need to scrap and learn to pick up points where they can.”
The former defender turned pundit is also concerned about the behaviour of Spanish manager Martinez, with post-match press conferences setting off alarm bells.
He also suggests that perhaps Martinez could do with adding some more experience to his backroom staff, as currently those at the club aren’t experienced enough or aren’t accustomed enough to working at a big club like Everton.
“Martinez is starting to look a bit lost in some of his post-match interviews,” added Keown.
“He seems to be more focused on games coming up rather than the games he’s just had. I don’t know if Martinez would benefit from some more experience on his staff or those who more used to working at a bigger club, because Everton are huge.”