Kyogo’s 33rd-minute winning goal looked offside, Hearts winger Barrie McKay was struck by missiles from home fans, and referee Bobby Madden stopped play and gave Celtic possession because their winger Jota suffered a hamstring injury running with the ball.
Hearts manager Neilson was flabbergasted at the officiating but, having already served one touchline ban this season, he could not be as forthright as he wanted.
“I’d end up going to jail if I said what I really think about it,” he commented when asked about the Jota incident.
“I’ve never seen anything like it in my life. The boy pulls his hamstring and the referee stops the game and gives them the ball back when we’re going to counter-attack. But that’s Scottish football, you’re in Glasgow.”
Neilson added: “I have two emotions – frustration because we got done by a poor decision for the goal. The second one is pride in the players because I thought we played exceptionally well, especially in the second half.
“I thought we pressed the game, got up on it and had belief in ourselves. We came here in the cup three months ago in the cup and couldn't get in the game. Tonight's performance is what we need to get to and we need to do it consistently. And we need to score goals off the back of it.”
Asked about the goal, he replied: “It's offside. The linesman [Alan Mulvanny] has got to make the decision. It's a key decision in the game. He doesn't make it. He is looking straight along the line, he can see he [Kyogo] is offside and he doesn't put his flag up. That's the disappointing thing. I've seen it again. He's ahead of the ball. He is offside.”
Hearts appealed for a penalty in the second half when Gary Mackay-Steven fell inside the Celtic penalty area. Neilson said: “There was frustration at some of the other decisions going on at that time. The goal was the biggest frustration.
“On Gary's one, I can see Bobby's point. There is some contact there, he is still going through and then Liam Boyce has a great chance to score. Does he bring it back after and give a penalty and a red card? Probably not but there were a few decisions there that were strange to say the least.
“Bobby said he [Mackay-Steven] clipped himself. I've never seen that before.”
Neilson said he didn’t see objects being thrown at McKay at corners. “Somebody in the tunnel asked him if he got hit on the back with a bottle. I don't know the ins and outs so I'm not going to say too much, but it's disappointing.”
The controversy somewhat overshadowed an encouraging second-half display by Hearts. Neilson added: “I said my piece after we were at Ibrox and then I had to write a report [to the Scottish FA] to explain what I meant by it. I can't be bothered doing that any more.
“It shouldn't be like that but that's the way it goes. We have to come here [Celtic Park] and play doubly well to get the points.”