How can I shut off circuits when I have a generator with an automatic transfer switch?
The load center with the transfer switch (or "critical load panel") should have a circuit for each circuit that was specified to be connected to the generator.    The original breakers no longer function because nothing is connected to them now; there is probably one dual-pole breaker feeding the critical load panel, and there should then be a breaker for each circuit there.

If you are not comfortable investigating, call the electrician that did the install and ask them to walk you through operation and service requirements for the setup.