A first-half brace from Jarrod Bowen was enough to sink the toothless Toffees, who’s 15 points from their first 20 league games is the worst return at this stage of the season in their history and leaves them in the relegation zone.

It came in front of the watching Everton board and owner Farhad Moshiri, who have come in for heavy criticism from fans in recent weeks as their season stumbles from one defeat to the next.

"Those things (whether he is sacked) is not my choice, it is my job to work, focus and keep my head down," Lampard told SkySports. "I have confidence in how I want to coach. There's difficult conditions that I am aware of.

"I just do my job and talk about what I can affect, and that's the players trying to get the right results."

Lampard says his relationship with the board has not changed through the difficult run of results.

"I know there are issues. I'm not trying to close my ears but as a coach it is not significant. They communicate (with me) and have done all the time I have been here. It is not my job to make them public."

Lampard felt his side deserved more from Saturday's loss, even if they only managed two shots on target.

"We had a lot of the game, the way West Ham play they afford you the ball at times. We moved it well but we have to be more clinical. We missed some chances and weren't dynamic enough. They had a couple of moments where they were dynamic and it changed the game."

Everton are next in action at home to league leaders Arsenal on Feb. 4, followed by a Merseyside Derby at Anfield. Lampard has vowed to fight on.

"(I’ll) keep working, the only way I know. Working at the training ground, going again. We have to be better as a team.

"If you score it can give you give a good feeling, if you don't the feeling is there for the other team and that happened with West Ham."