Neilson was forced into a late signing ahead of Sunday's derby win over Hibernian when Scott Gallacher, who was to make a full competitive debut after Neil Alexander fractured a cheekbone during the win over Rangers, picked up an ankle injury in training.
Lee Hollis, the former Motherwell goalkeeper, joined on a short-term deal last Friday but Neilson opted for Jack Hamilton - whom he recalled from a loan at Stenhousemuir - in goal for the 2-1 win over their city rivals. However, with 20-year-old Hamilton cup-tied for tomorrow evening's Petrofac Training Cup tie at Livingston, Neilson is left with untried 17-year-old Robbie Brown as cover for Hollis.
"Lee will be here and we've got a couple of guys lined up who could possibly come in to help us out short-term," Neilson said. "We'll take a look at it and see what we do. Jack's cup-tied for the midweek game.
"We sent him to Stenhousemuir. We had the option whether we let him play him in the cup ties or kept him out. In hindsight we should have kept him out but I wanted him to play in bigger games. If Stenhousemuir had drawn Rangers or Celtic it would have been great experience for him. He's going to get opportunities this season. I'm pleased for him. But Lee is an experienced keeper. He played a lot of games for Motherwell."
Neilson also admitted that striker Dale Carrick is likely to be sidelined until at least the start of next month with a thigh problem. Carrick started the capital club's first two matches of the season against Annan and Rangers before missing the weekend's visit of Hibs.
"It's not the main muscle in the thigh, it's the lateral side," Neilson said. "It should hopefully heal up pretty soon. He won't make Livingston. They're talking about maybe two or three weeks, but we're hoping he will be back sooner than that."
Meanwhile, Vincent Lunny, the Scottish FA compliance officer, has until today to decide whether to issue any Notice of Complaints after the derby on Sunday. Lunny yesterday reviewed footage of the match and has until 3pm today to take action.
Tempers flared at the end of the game following an incident involving Hearts winger Jamie Walker and Hibs' Lewis Stevenson at the corner flag. With Walker attempting to waste time, the 21-year-old appeared to be caught on the back of the leg by the boot of left-back Stevenson.
In the melee that followed, Walker squared up to Stevenson and television pictures appear to show the playmaker moving his head towards his opponent, although it is unclear if contact was made. Lunny is said to be reviewing that entire incident to see if either player overstepped the mark.
The Hibs players, notably captain Liam Craig, were furious that referee Willie Collum failed to take any action against Walker.
Afterwards, Hibs coach Alan Stubbs said: "The lad put his head on one of our players. It will be interesting to see what happens."
Craig Levein was happy, at least. The former Hearts captain and manager returned to the club in the summer as director of football and has played a major part in helping to piece together the new-look coaching staff and playing squad since new owner Ann Budge brought the club out of administration in June.
Levein wrote on social media: "There's nothing like a full Tynecastle on derby day. Great atmosphere. Brilliant to send our supporters home happy. Tough match and lots of nerves on show but class told in the end. Forgot how much I love this fixture. Happy days."