Fired from IT company and not allowed to give notice period what to do

I was fired from a IT company in gurgaon after being in pip for 2 months.During exit I asked them to extend my pip or to let me serve the complete notice period of 3 months since I did not have a job at that point.They did not listen and relieved me on the same day.After coming out I had to face problems finding a job because every recruiter asked me as to why I left my job when I did not have any offer from outside.This also affected my health and I have been suffering from severe depression ever since my exit and living on antidepressants.Please advice if I can file a case against this organization for not being flexible and not giving me enough time to look for a job?