Neilson laid the blame firmly at the feet of referee Kevin Clancy, who dismissed defender Jordan McGhee for two yellow cards six minutes before half-time.
The Hearts head coach is angry at the decision and believes it changed the course of the game. McGhee received a second caution for a tackle on Edward Ofere but TV footage seemed to prove he played the ball fairly. United opened the scoring four minutes later and, after Jamie Walker’s 49th-minute equaliser, won the game with Paul Paton’s 25-yard drive on 88 minutes.
Neilson complained that Hearts are left frustrated by a refereeing decision for the second game in succession. Blazej Augustyn was dismissed for two yellow cards in last week’s Scottish Cup defeat by Hibs and McGhee became the seventh Tynecastle player red-carded this season.
“That’s two in a row now. You always hope these things even themselves out over the course of a year. It’s two big games and two key decisions that have changed the games,” said Neilson. “I’m sure Kevin will look at it and realise it’s not a second yellow card, but he gets caught up in it and gives it.
“If the referee makes decisions like that, decisions you believe are wrong, it’s not the players’ fault.
“McGhee goes in, wins the ball, studs aren’t up, not at pace, not reckless, no intent to endanger the player, so I don’t know where the referee gets it from. I don’t know what he sees. He obviously sees something different from us and makes a decision but it’s a huge decision in the game. It changes the whole game.
“We feel aggrieved that we worked really hard and got nothing. The strike at the end is one where you need to hold your hands up. He [Paton] has smashed it from maybe 30 yards so it’s difficult to stop it.
“The turning point of the game was the red card. When the referee makes a decision that nobody else in the ground sees, it baffles you. He’s the guy who takes the money, he’s the guy who makes the decisions so we just have to accept it.”
McGhee is now suspended for this weekend’s league match with Kilmarnock at Tynecastle.