Hi Sasha,
Your sentence: "I'm sorry, but there are _________ tickets left."
Here, you need a determiner to provide some information about a quantity, and "no" can be used as a determiner for that purpose.
"None" is not an appropriate answer here, because it is not used immediately before a noun.
Examples (incorrect): There is none tickets. There is none response.
However, "none" can be used with "of + determiner + noun". So, if you really wish to use "none", the sentence can be modified as: "None of the tickets was left."
I hope this helps you.