Something I've not seen pointed out elsewhere too, is that (unfortunately) this is an answer that every manager of every large company has ready at the tip of their tongue. It pops out from rote memorization. Not about women, but about all employees: "We only give raises as part of the normal annual review process. I understand you think your compensation needs to be reconsidered because ...... and I'll make sure to discuss that with the rest of the management team at review time." It's not good, but it's a well rehearsed blow off answer for which every manager is trained.
I think he's a good guy who is handling the aftermath well. He gave a stupid answer and apologized. I honestly the bigger mistake is telling employees to trust the system, rather than a single off the cuff answer that didn't fit well.