Neilson's side trailed at half-time after Ross County skipper Blair Spittal hit a double in response to Liam Boyce's early strike.
But Stephen Kingsley levelled midway through the second period to earn Hearts a 2-2 draw.
Both sides had chances for a winner in an entertaining encounter and although Hearts missed the chance to top the table on Saturday night, Neilson remains encouraged by his side's return to the top flight.
They now host Livingston and Motherwell in their next two games and Neilson wants them to utilise their home advantage.
"There's massive positives," he told Hearts TV. "Six games in, we are undefeated, we were sitting joint top of the league and we just need to keep trying to win games. We are playing good football, scoring goals and creating chances.
"The key thing for me is, if we don't win the game, we have to make sure we take a point and move on to the next one.
"Home games are so important for us this season, we have two coming up and we have to make sure we win those games.
"Coming away from home, we want to win every single one, but if we're not going to win it we take the point and move on."
County came close to a late winner when John Souttar cleared off the line from Joseph Hungbo and manager Malky Mackay also had plenty of plus points.
His side could not have had a tougher start to the season with the visit of unbeaten Hearts coming on the back of playing last season's top five.
Following a Covid-disrupted preparation and a major turnaround in players, a return of three points has given them a solid platform to build on.
"I have to give great credit to the players, they are taking on board the information we are giving them," Mackay told RCFCTV. "They are fit, because they are having to work as hard as they are for 90 minutes. They are looking organised.
"There are players making their debuts every week, Ashley Maynard-Brewer came in for his debut in goal and was fantastic. They will start to get to know each other better and settle in.
"We have played the top five and created good chances against Aberdeen, Celtic, Hearts, Hibs and Rangers."
On-loan Charlton goalkeeper Maynard-Brewer made several good saves after being given his chance ahead of Ross Laidlaw.
"We were delighted to get Ash," Mackay said. "He was just back from the Olympics with the Australian team but he came up and trained like a beast for his first six weeks and shown real quality. He has a big personality as well which is important for a goalkeeper.
"The first goal takes a huge deflection off Jack Baldwin and the second goal was real quality. Overall he was excellent."