The German midfielder was replaced by Alex Iwobi after struggling to influence the game, as Phil Jagielka’s strike delivered a huge blow to the Gunners’ top-four bid.
Ozil trudged off in frustration and appeared to throw a strop on the bench, launching his jacket in the direction of Toffees manager Marco Silva.
And according to former Wimbledon hard-man Jones, Ozil lacks the character to lead a team in such a hostile environment.
“Ozil, captain? He’s never a captain, for me,” the footballer-turned-Hollywood star told talkSPORT.
“I wouldn’t want him leading me out at Everton away.
“Goodison Park is a hell of a place to go. It’s a fantastic stadium and the crowd really get behind them.