Having lost 1-0, to a penalty conceded in near-comical circumstances by a distraught Jordan McGhee, the Tynecastle side missed the opportunity to close the gap on the Dons and have instead slipped seven points behind in third spot in the table.
The Gorgie men, back in the top-flight after winning the Championship at a canter last term, have now gone three games without a win but, with almost half the season gone, still appear to have an excellent chance of clinching European qualification.
And, rather than being damaged psychologically by Saturday’s last-gasp defeat to Adam Rooney’s 87th-minute penalty, Neilson reckons the blow could make them stronger.
The Hearts head coach said: “It’s good that we’re part of games like that. Eighteen months ago we weren’t, 18 months ago we were struggling.
“Now, we’re [going to Pittodrie] and losing 1-0 – and being devastated. If anything, I think it will have a positive impact.
“We’ve gone to Pittodrie and possibly could have won it. And we’ve lost from a mistake, a mistake that any player could make, and it’s just something we’ll have to accept.
“We’re still working hard, we’re still in a great position and we just have to try to continue that.”
Meanwhile, Hearts legend John Robertson reckons McGhee will have felt physically sick after handing Aberdeen the points. The 19-year-old inexplicably threw up his arm to handle Kenny McLean’s cross under very little pressure and instantly knew he had committed a massive blunder.
Robbo told Sky Sports: “Hearts looked comfortable in the last 20 minutes. Defensively, Jordan McGhee had a really good game along with the other lads in the back-four.
“Then, obviously, he has his moment of madness which has cost Hearts the opportunity to take a point. I think, on the second-half showing, it was harsh on Hearts.
“With everything that Hearts put into the second-half, they probably deserved a point.
“But Jordan will be inconsolable. He will probably have felt physically sick and asked himself the question why he did it.
“He had a terrific game up to that moment in the match.”