The Easter Road side struggled at the start of the campaign, suffering a 9-0 aggregate defeat by Malmo in the Europa League qualifiers before Scottish Premiership losses to Motherwell and Edinburgh rivals Hearts.
Pat Fenlon's side have recovered to go on a four-game unbeaten run but the two wins in that sequence have come away from home to Kilmarnock and St Johnstone.
And with only one league win at Easter Road this year - against Dundee in May - Nelson believes it is time the Hibees' diehards are rewarded for their loyalty.
The Hibs defender, 33, said: "We don't mind where we pick our wins up but it is massively important that we start picking wins up at home for the fans who buy season tickets and come week in, week out.
"We are really focused in trying to turn Easter Road into an intimidating place for teams to come to.
"We don't set up any different away from home, we don't sit off and try to get them on the counter attack.
"Maybe other teams come here and do that so maybe that has something to do with it.
"If we can start the game positively and get an early goal against teams who do that, then their game plan goes out the window and hopefully we can go and win comfortably.
"But it's not a case of if we don't get a goal in the first 15 minutes then that's it, doom and gloom. You can win the game in 92nd or 93rd minute.
"It is about patience, you don't want to go out kamikaze from the off and go one down within 20 minutes.
"I'm sure the fans will stick by us and once we get that first home win, they become a little more patient and we get another win and it snowballs.
"So it us down to us to get the three points which will relax everyone a bit more."
Fenlon is hoping the further confidence taken from last week's win at St Johnstone, where they came from behind to win 2-1, will help get three points against the struggling Buddies.
He said: "You can see the confidence coming back into the players and training has been good this week but we need to back that up.
"It is important on the back of winning away. If we can add the home form to the away form it becomes really good."