Speaking personally, I wouldn't have got a wink of sleep anyway - knowing that my complete plans/flights/New Year's eve celebrations were depending upon a single wake-up call booked at reception would have been enough to keep me awake all night....or at least waking up every 15 minutes throughout the night to check my watch.
I'm really sorry that you missed your flight and celebrations, but it really was a crazy plan! I mean, if you stay in lots of hotels you must have had the odd missed wake-up call in the past? I know I have on numerous occasions, and I don't stay away nearly as much as some of the seasoned travellers here. I would never trust a hotel wake-up call alone for something like this.
I do think that the hotel management could at least say sorry for it, although I'm not sure that they need do much more than that. I think anything else would be a bonus frankly.