Kenwright and the Toffees board have come under criticism from supporters for their lack of funding, which halted the Premier League side from purchasing any players in the last summer transfer window.
"The only negativity there is is because of how the team play," said Moyes. "We have not played well enough. It is nothing to do with the board of directors or the chairman, it is to do with me and the team."
Everton, who sit eight points above the drop zone, signed Manchester United midfielder Darron Gibson earlier this month.