The manager said players must look in the mirror as Tuesday’s Scottish Cup loss at Brora Rangers was followed by Queens’ first win at Tynecastle Park since 1963.
A group of fans demonstrated outside Tynecastle before the match to demand the removal of Neilson and the Hearts owner Ann Budge
“We understand the frustration,” said Neilson. “There’s nobody more frustrated than me, that’s for sure, after Tuesday and today. It’s probably not the time to do it as a mass group so we would ask them not to. I totally understand their frustration because I’m the same.
“There will be a lot of conversations to be had. We had one there after the game about how we need to look in the mirror. We have to pull ourselves together.
“We are 13 points clear and it’s been a big blip over the last five days but we need to stay strong and keep the group together to make sure we get our focus back.”
Queens went 2-0 up through a Connor Shields double before Hearts fought back to 2-2 with goals from Mihai Popescu and Armand Gnanduillet.
However, Andy Irving’s late own goal proved costly. Gnanduillet had the ball in the net again from Jamie Walker’s cross but it was disallowed because assistant referee Alan Mulvanny’s flag indicated the ball was out of play first.
“It’s a big call. I’ve watched the video and the assistant is seven or eight yards away up the line, so he’s just guessed,” insisted Neilson. “I think it is in. It’s disappointing that an assistant will guess on that. He is clearly up the line and can’t see.
“We spoke about getting a reaction after Tuesday night and we’re a goal down after a minute with an individual error.
“That hit us a wee bit, then we lost another poor goal when we stepped out and the ball went over the top. To be fair, we fought back to 2-2.
“We were trying to win the game and there is another individual error that kills us, so I’m really disppointed.”
With doubts surrounding his own future, Neilson must now try to pick the Hearts players up. “It’s crazy that we’re talking about confidence in the group when we’re 13 points clear with five games to go. If you had offered us that at the start of the season, we’d have bitten your hand off,” he said.
“We’ve had a wee blip, the last five days have been really difficult for everyone. It’s a case of sticking together and making sure we get over the line.
“We said at the start of the season that we had to turn round a big ship that’s struggled for the last two-and-a-half to three years. There will be blips on the road.
“This last five days have been tough but when we reflect on where we are, we need to try and move forward.
"We will get Michael Smith and Craig Gordon back [from international duty], which will add strength and security to the team. I don’t think our keeper Ross Stewart could do anything for any of the goals today.”