I'm sorry you lost your betta
Are you saying you're pretty sure he DID have ick, or that he did not have ick? If you think he had it, yes, that will kill a fish if it's not treated.
Also, bettas really do need a heater and a filter. Plus the tank needs to be cycled so that there's enough beneficial bacteria to keep the water safe for the fish. We keep our bettas in 2 divided 10g tanks and the temperature stays around 80. They like a pretty warm tank -- quite a bit warmer than room temperature is recommended.
Again, really sorry about your fish. I hope you will have better luck in the future. They're such neat fish!