The Toffees suffered yet another setback in their attempt to save their Premier League status after being beaten 3-2 by fellow strugglers Burnley away from home.
The loss has put further pressure on Lampard, who has failed to make an impact in charge and there are now question marks over his position.
Stubbs though believes that sacking Lampard is not the solution, with the focus needing to be on the players, who need to step up.
“There’s a few fans saying Frank Lampard has got a few decisions wrong”, Stubbs said on Sky Sports.
“But at the end of the day, these are the same players who have been with the managers before him. It’s not about getting rid of Frank Lampard now
“It’s about the players trying to do whatever is necessary to get a result and get Everton out of the mess they’re in.
“Too much blame has been placed on managers but there is so much wrong at Everton right now – from boardroom level right the way through to the pitch.”
Stubbs feels the need for the players to bring that extra desire and spirit that will be needed to save Everton’s season.
“The players have got to somehow find enough desire and spirit to get Everton through this season and keep them in the league.”
The 50-year-old believes relegation to the Championship would be like a doomsday scenario for the club and admits he is worried.
“It is perilously close to the doomsday scenario.
“This is the most fearful I’ve ever been as an Everton fan.”
Everton now have yet another uphill battle in the offing when they take on Manchester United at Goodison Park on Saturday.
