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Neilson and assistant Stevie Crawford signed new deals to take them up until the end of season 2017-18.
Saturday's 1-0 win over Kilmarnock moves the Edinburgh club 11 points clear in third place.
"I think there's a long way to go at this club and I want to be part of it," Neilson told BBC Scotland.
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"There's potential to keep building and take the club to where it belongs.
"That's the long term goal [to try and win the league]. It's not going to happen overnight. We need to try and build the young players coming through. We have to balance it off with selling players and producing our own and bringing good talent in."
Hearts missed two attempts from the penalty spot as they were made to battle for all three points at home to Kilmarnock, with Jamie Walker managing to score on the rebound from his effort.
"It's good to get three points against a tough team," said Neilson. "We had a couple of chances to kill the game off, it's something we need to improve.
"It gives us a lift after the disappointment last weekend at Dundee United.
"There will still be a lot of twists and turns before the end of the season, everyone can beat everyone in this league. You see today we're playing second bottom and really had to grind out a 1-0 result. Dundee United go to Ross County and win 3-0 so it just shows you there's a good standard here."
Kilmarnock manager Lee Clark thought his side played well enough to earn at least a point but said his players have much to improve on if they are to avoid the relegation play-off.
The Rugby Park men are two points adrift in 11th, while Dundee United closed the gap at the bottom to eight points, with Mixu Paatelainen's men having a game in hand.
"We're disappointed with how we've given the penalty away," said Clark. "It is a penalty. I'm disappointed we haven't done more to help out our goalkeeper after a terrific save.
"In our predicament we need to get results. Good performances and not getting points on the board aren't sufficient for us.
"I've said to the players I think we've wasted the first half because we were waiting for things to happen rather than making them happen. We did that better in the second half.
"Our defensive displays have been good. We've given a disappointing penalty away, two disappointing penalties really. We've had lots of possession, lots of situations, but we need to work the goalkeeper a lot more."

Police were called to reports the Stagecoach bus had hit the bridge at Chapel Hill, near the train station, shortly before 14:00 BST.
Two people were on board the bus at the time, but were not injured.
Chapel Hill has been reopened. Network Rail said train services between Basingstoke and London, which use the bridge, had not been affected.
Hearts head coach Robbie Neilson says he extended his Tynecastle contract because he wants to lead the club to the Premiership title.
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The roof of a double decker bus has been torn off after it struck a railway bridge in Basingstoke.