Personally, I probably wouldn't say anything to the teacher, or the other mum...but my DD is unlikely to be bothered by not being invited to a party.
DD knows full well, that when she has her parties, she has a maximum number of people she is allowed to invite (usually no more than half the girls in her class) and she has to choose which girls she plays with the most. she knows full well, that it doesn't mean that she likes the girls who do not get the invite any less, just that I can't afford to invite everyone so she has to choose.
Therefore, when she is not invited to parties, we explain the same thing - that mummies can't afford to pay for every child to come, and so the birthday child just has to choose a few of their friends to go. Thankfully, to date she has not been excluded by any of her best friends, so she is not bothered when other children do not invite her, because they are not usually her closest friends iyswim!
I've never made a big deal out of such things, and almost gone the other way, so now DD doesn't expect invites (apart from close friends) and was once asked if she was going to Xs party, to which she replied "No, why would X invite me, I don't play with her"
My brainwashing is working.... 