Notice period - how to handle our situation

[Kishore Babu]

Hi, 
Our rental property is in Manteca, California and our rental property tenants vacated couple of weeks ago after his lease expired on Dec 31st 2023. They stayed for 2 years and our rental lease agreement indicated to provide two months notice period for which they agreed but tenant didn't give us any notice. When we questioned him about it and asked for two months rent compensation, he argued with us saying he mentioned during the last lease renewal that this is his last lease with us over the phone. However we don't remember that was the case. 

May I pls know how can we proceed in this situation.  Can we request him two months compensation?. Is the notice period given over the phone an year ago (which I don't remember) considered as notice period.

rgds

Kishore