Lampard was hoping for a key win at Goodison Park over fellow strugglers Southampton on Saturday, but the Saints grabbed a 2-1 win to put Everton deeper into trouble.
Everton are second bottom of the Premier League table and only kept off the bottom by virtue of goal difference.
Fans are unhappy with the club’s board and Lampard is working with a tight budget when it comes to trying to strengthen his squad in this month’s transfer window.
Gray, asked whether if he was in Lampard’s position he would resign, admits he would seriously consider it and believes that Everton have gone backwards under the former Derby County boss.
“If I’d been there a year, and he has, and I’ve had two transfer windows, and I’ve shaped the team the way I want, within restrictions”, Gray said on beIN SPORT.
“Plenty of players have come in with Frank since Frank’s been there, so it’s his team.
“And I haven’t moved them forward, if anything we’ve gone backwards.
“I would seriously say, you know what, maybe this is for someone else, maybe somebody can do a better job than me.”
Lampard must lead Everton to face his former club West Ham United, who are also deep in trouble in the Premier League, next Saturday.
