Saying that Brexit is the cause of something based on one's experience with clients, expressed in a way that suggests that it did not positively or negatively affect themselves in any way, does not strike me as particularly bitter, but suit yourself.
First, nothing about "y'all have to thank" suggests that they consider the person they are responding to responsible for Brexit, which is a requirement for it to imply that they are putting some sort of blame on the person (or the collective group they represent).
But let's for the sake of it accept that "it's your own fault" is what was meant by it anyway. That still doesn't imply bitterness.
If parents explains to their child not to run with scissors because they might hurt themselves, the child does so anyway and ends up hurting themselves, and one of the parents says in-between consoling their child "but do you see how you only have yourself to blame for it, if you decided to do this anyway after we warned you this would happen?", then that might not be the most considerate timing for sharing a harsh truth, but there's nothing bitter about the statement.