Rangers midfielder John Lundstram gave the hosts a deserved interval lead in the cinch Premiership top-of-the-table clash with a wonderful shot from 30 yards with six minutes of the first-half remaining.
However, in the final minute of normal time, a mistake from Gers goalkeeper Allan McGregor from a Gary Mackay-Steven corner allowed Jambos defender Craig Halkett to head in the leveller which keeps Neilson's side unbeaten in the league after nine fixtures and still one point behind leaders Rangers as they start preparing for the visit of Dundee next Saturday.
Neilson, who was sent off by referee Don Robertson three minutes from the end for dissent following a touchline altercation which saw Tynecastle defender Stephen Kingsley and home substitute Juninho Bacuna booked, told Hearts' official Twitter account: "We wanted to go and win but the worst-case scenario, you take a point.
"We had periods in the game where we had to fight really hard to get control and periods where we were in control and passed it really well, especially in the second half - I thought we were excellent.
"You take a point against Rangers, you've got to win next week, the week after that and the week after that so we know that. That's the most important thing.
"We are at that top end of the league and we need to keep winning games and it all starts on Monday.
"For me it's about the next game. There is no point in going there and getting a point and then not beating Dundee."