Moyes goes into tomorrow's derby with Liverpool with doubts over his future.
But he rapped: "It's nonsense. I've been here 7½ years and worked really hard to get here. I'll carry on trying to get through this as well.
"If the fans thought it wasn't David Moyes they wanted, I would have to think. But at the moment I need to keep working hard with the players.
"We've not done anything different with the same bunch who finished fifth. We're not trying anything weird and wonderful.
"I'm the man responsible for signing the players and they should be shaking my hand and thanking me for giving them the chance to play for Everton.
"It's such a great club and for some of them it might not get any better."