Why do HRs do this and how can I negotiate? 😔

So I basically cracked an offer for 11.5 LPA from TCS. I have 4.5 years of experience as a frontend developer React.js. After TCS i also cracked Accenture right after it while serving notice period and the HR asked my expected salary and I told him 16LPA. He asked why this expectations and I told him that I already have an offer from TCS of 11.5 LPA fixed and that in my interview I was told that expectations would be to handle both frontend and backend.

The HR told me that ok you send me your offer letter from TCS and I will definitely give you a better offer. The next day I received an offer letter of 13.9LPA CTC where the fixed component is 11.5. I'm like WTF?

I contacted him and told him that I don't think this is a fair offer and the person told me that you'll be getting more benefits and TCS has included performance pay which won't be 100% always (which I told him would be 100% as I've verified it with the HR and my friends and it's given quarterly whereas the bonus is given biannually in Accenture and varies). He said ok I'll check and get back to you but he never did. Neither did he reply to my emails.

Is this the correct offer for me? I really want to touch that 1 lakh per month salary. 😢