The brothers refused to wear T-shirts supporting the anti-racism campaign last October due to the length of suspensions handed to Chelsea captain John Terry and Liverpool striker Luis Suarez for racially abusing Anton and Manchester United defender Patrice Evra respectively.
"The danger of serialisation of the book was that they are my personal opinions at that moment in time," Carlisle told Sky Sports News.
"So when the whole Kick It Out boycott kicked off, that weekend I did not understand what was going on. I did not agree with what was happening and I voiced that in all the interviews I did.
"But as you read the rest of the book, [you can see] the issue evolved and we talked about what they were bringing to the fore and the reasons why they did that. I did then come to understand."
The Football Association have since introduced a minimum five-game ban issued to players found guilty of racism.