Given you are unsatisfied with the resolution, the next thing to do would be to contact the email you mentioned. I would definitely recommend saying that xyz was not good, you spoke with x person at the hotel who is the front desk manager, and feel that their response was not near the level you expect from the Hyatt brand. From there, it’s your choice how you want to proceed with the email, but generally would recommend against requesting anything specifically. Say that you normally love Hyatt and rarely have issues, so this threw you off. Say you are reaching out both to help provide feedback to improve the property, and because you felt the management did not provide an adequate response. The friendlier you are, the better the result tends to be.

Customer service often takes into account not only your email, but also your history and current status with them when deciding how to compensate you. They will also take into account the chances of you returning to the property and/or staying with Hyatt again. Don’t go in expecting anything specifically, but I can tell you that Hyatt corporate has treated me far better than any other brand when it comes to proactively dealing with complaints.

Good luck!