However, Howard believes that supporters were wrong to heap verbal abuse in Moyes's direction.
"We have brilliant fans, but that was unfair on him," the American goalkeeper is quoted as saying by BT Sport. "He was the second coming, the messiah 12 months ago, and I don't think as Evertonians we should ever forget that.
"I love David Moyes. I think he is a brilliant manager. He was [a brilliant manager] here for us and I will be forever grateful to him. Football is a funny game. It has highs and lows. You take the good with the bad and you keep rolling."
Everton are currently fifth in the Premier League table, 12 points ahead of seventh-placed United.