McLeish has been left frustrated at Villa's failure to kill off opponents when in control as demonstrated by last week's 1-1 draw at Blackburn who conceded a late equaliser.
But the Scot believes Villa are not suffering any mental hang-up about their failure to win in front of their own fans. McLeish said: "It (a home win) has been too long to be honest. But someday a Villa team will win again at home so why can't it be on Saturday?"
He continued: "We know we are playing against a pretty slick Fulham side with lots of quality but nobody is unbeatable in this league.
"If I was to sleep every night without waking up and thinking about it, I wouldn't be human, and I shouldn't be in the job, so we want to win and we want to win at Villa Park."
McLeish added: "You can only say it affects a player's mentality if it continues to happen although I think we've been unlucky in one or two games.
"But I also believe we have shot ourselves in the foot with back passes, own goals and that kind of thing and that has blighted us a little bit.
"We've got to get back to getting those shut-outs. If we get a goal when we are on top, let's get another one. Let's show ruthless professionalism.
"That means both in the attacking sense and defensively.
"If we can't quite get another goal, then make sure we don't lose one and we have probably let ourselves down a bit this season."