Then I don't think he does get it. Yes immigration was part of it, but I think a larger part is a sense of the left behind - that large swathes of the population see themselves failing to benefit from economic growth while other chunks are doing very well thank you very much. What Blair's done there is both lump the Brexit vote into a single immigration related box AND dismiss it entirely, all in one - feeding the feeling that the elite don't give a damn - the exact reason I think a decent proportion of Brexit voters went that way. What's more, if he was right in his analysis, he's failed to make the case for increased immigration in terms that would persuade the disaffected.
The thing that really gets me about Blair though, is that he seems to think that by piping up he's helping the causes he espouses when I don't see anything but harm. He doesn't seem to understand how heavy the baggage he carries is.