So he should be, after sticking the nut on an opponent last week and getting red-carded while Accies' title hopes momentarily went up in red mist. I'm cackling about it all now, with Neil sitting right in front of me, though he wears a more solemn expression.
"I shouldn't have got involved," he said, looking back on last week's 4-1 defeat by Dumbarton. "It was a heat of the moment thing. I was frustrated, because we'd created so many chances but were behind.
"Over my career it has been one of my biggest strengths, but also maybe my biggest weakness: my aggression. I've often got myself involved in things I maybe shouldn't have, but it has helped me against better opponents, you know, where you've got to dig in. I've spoken to my players, I've apologised to them, and I've fined myself over it all."
Really, I ask, you've fined yourself? Come on then Alex, how much?
"I took 24 players out for a three-course lunch, so you can work it out for yourself," he replies. "It is a considerable amount I'm down." With one hurdle to go today, against Morton at New Douglas Park, and after a fine season, the Accies manager is doing penance.
I've always liked Neil as a player - skilful, hard, mostly fair - though he does have a bit of a "reputation". To his own surprise he has now been nine years with Hamilton, as the team's fixer, leader, enforcer, and now manager. I dared to ask Neil if he thought of himself, as some others do, as a dirty player, wherein his response was quite revealing.
"No, I don't," he replied. "Until three years ago my disciplinary record was pretty good, but not so much now. The game is a lot stricter, the old 'professional foul' is now an automatic booking, which is a problem for me, because it has been so much a part of my game, in terms of the old tricks of the trade. So now I find myself getting in a wee bit more bother than I used to.
"I regret what I did last week - I maybe prevented us from taking something from the game. So I'm eating some humble pie. I'm taking any criticism on the chin. This is the most press coverage Hamilton have had in a while."
Today, Dundee, with a two-point lead at the top, will face Dumbarton at a bulging Dens Park, while Hamilton take on Morton. It is a thrilling championship finale and Neil has done a terrific job in his first full season as a player-manager, at the age of 32. How has he done it, and with such a young team?
"I can relate to my players," he says. "I believe in them, I have faith in them, and they know that. I've been captain here for a long, long time so I understand this club. I keep telling the players: 'Give of your best, and don't give in.' That's all I ask, and I think the players respect me for that.
"I always wanted to coach and pass on my knowledge to young players. Whether I'd be a manager or not, I wasn't sure. But I got some fantastic coaching opportunities under Billy Reid, especially when he asked me to nurture James McCarthy and James McArthur. That probably helped me on my way as a coach. To be honest, I just wish my management career had started a few more years down the line. Simply because I want to play. I love playing. As both a player and a manager, you can't really enjoy the final years of your career, you've got too much going on. But fate has thrown me this hand and I'm happy to take it. I shouldn't say this, but I'd do this job for nothing, it's so good, so enjoyable."
Neil is actually amazed he has made it to nine years at his club. When he first signed in 2005 he could never have imagined his stay would last so long. "I wasn't going to sign for Hamilton - it was my wife that convinced me to do so. We came back up the road from England for domestic reasons - she wanted home to Coatbridge. I'd had a great five years with Barnsley and, when I came to Accies at first, the professionalism here wasn't the best. I thought, 'what am I doing here?' I'd played in the Championship in England - quite a high level - and so it was very different coming in to Accies.
"But then Billy [Reid] really got things moving, and I enjoyed it so much under Billy, I just stayed and stayed. I've never left. I saw guys like the young Jameses coming through, and it really spurred me on. I wanted to stay to help the team in the SPL."
Reid looms large in the Neil psyche, with good reason. The wee, bustling, ex-Hamilton manager was a mentor and a friend in every sense to the club's current player-manager.
"The biggest influence on me is definitely Billy. It still gripes with me that, when he needed me most, during that final, difficult spell for him here, I wasn't available to play for him. He looked to me to help fix things on the park. He had faith in me, he trusted me. He was great to me, we really respected one another.
"Any time I played I put my body on the line for him. I'd run through a brick wall for Billy. I think that's why I picked up so many injuries. And he always backed me. He used to tell me I was the best player in the SPL. He'd tell me that all the time."
Meanwhile, Neil knows that Hamilton aren't everyone's cup of tea to be taking their place in the Premiership, should they go up. With just 300 season-ticket holders, and average crowds of 900, some say the top tier's brand will suffer.
"There is this myth that we were getting crowds of 3000 here," Neil argues. "We've never had crowds like that, or rarely. Our crowds aren't down significantly - maybe by 400 or so. What I would say is, other teams coming here used to fill the away stand - St Mirren, Morton, St Johnstone, Dundee - they all used to bring a good crowd with them. I think the away crowds and the home crowds together have dropped a bit. It's the financial climate we're in, isn't it? Money is not flush.
"Also, look where Accies are. We're possibly in the worst possible place. We're sandwiched between Celtic and Rangers and Motherwell and all these other clubs. It's difficult for us to attract fans. It's always been that way for Hamilton.
"Going up would be a great achievement - but I'd be lying if I didn't say I feel a wee bit disappointed. We had it in our own hands last Saturday. We were the better side against Dumbarton, we should have won the match."
You're saying it, Alex.