The hosts twice came from behind at Tynecastle to earn a point against the league leaders, with their second equaliser coming in stoppage time through an Osman Sow strike.
However, Neilson believes that his side should have claimed all three points from the contest and bemoaned the two "slack" goals that they conceded.
"I spoke to the players as soon as I went in and the first thing I asked them was if they were happy with a point and to a man they said no. They feel that they want to be winning games like that," he is quoted as saying by PA.
"They had a great opportunity to take three points but we gave up a slack goal in the first half and a bit of slack play lets them in in the second half and we had to fight back twice. It shows the distance we have come in 18 months that the players are disappointed not to take three points against Celtic, the top team in the league but that's the aim.
"But we still have a distance to go, we want to challenge and push as hard as we can and it will take a year or two to try to build with this team but it is definitely something we can do."
Hearts, who remain 10 points adrift of Celtic in third with the draw, take on Dundee United on Wednesday evening. body check tags ::