Arsenal boss Mikel Arteta finds himself under increasing pressure with his team sitting an unthinkable 15th in the table after their worst start to a league campaign since 1974.
They have 14 points in as many games and have scored just 12 goals, sitting only four points clear of the relegation zone having played more matches than the bottom three.
"I wouldn't be so sure [they will stay up], Shearer said to BBC Sport.
"Not with that starting team and the attitude of some of those players.
"Awful - no creativity, players going through the motions, not working hard enough and not closing down.
"Mikel Arteta should be a worried man relying on that group of players trying to save his job.
"Twelve goals all season, they have no options. Arsenal are never going to score goals playing like that."
Nicolas Pepe scored a penalty for the Gunners but last year's £72 million signing was one of the players singled out for criticism by Shearer.
"Against Everton, Pepe was not prepared to get into the box," added Shearer.
"[Pepe] was jogging, sometimes walking. He has got to do more.
"There are a few players in that team who are not giving everything for the manager."
Speaking after the game, Arteta acknowledged there would be further uncertainty over his future with the FA Cup winners.
"I understand that," he said in response to a question about his job being under threat.
"My energy and my focus is only on getting the team out of that situation, maintaining the spirit on the team and the fight the boys showed every time they go on the pitch. You can see that, you cannot deny that.
"Obviously, again, the results - there is no question about that, it's not good enough and it's not acceptable for the standards of this football club."
Just when Arsenal could do with a favourable run of fixtures, they have the opposite.
The Gunners are at home against Manchester City in the Carabao Cup next before they meet London rivals Chelsea on Boxing Day to resume their league campaign.