As a manager, you are never going to please everyone.
My advice for Neil would be to avoid confrontation with supporters, try to focus on the game and put things like that to the back of his mind.
I would hope there was no bad language used by the fan in Saturday's spat between the two and that the attack was not of a personal nature.
Celtic fans as a whole are right behind Neil and he is admired highly by the majority of the supporters – and rightly so because he has done a very good job in the time he has been at the club.
I would also say to Neil that he could lose his job without volunteering to lose it. I know he will be frustrated but the Celtic post is a great one.
You can't buy experiences like the one he had against Barcelona and he won't want to give that up easily.