Generally, yes. But there have been cases where exceptional performers (including some from NLS) were promoted to Associate and even Engagement Manager sans MBA.
I understand what you feel, but I'd advise working on yourself instead. Make a better version of you in as many aspects as you can, and you will find yourself less and less insecure and less and less interested in what people think.
They need analytical skills in numbers. Mostly, those from fiance backgrounds like CAs, MBAs or CFAs have them. If you want to join do one of these in parallel with your LL.B. Else just be prepared to work with words and arguments.
I am from a so called T1 NLU, my rank was within the top 10% of the batch, in my penultimate year, about 7 years ago, I had approached all the big consultancies in India, I managed to get into a conversation with the HR in 3 of them, the common gist is the need for MBA, except for Mckinsey but they would only slot you in law related dept. So, unfortunately, at least 6 years ago you would have needed MBA, you can try and contact the HR and check out what the requirements are.
BCG hired a person directly last year from nalsar as a front-end associate and has hired two more people this year. they don't have direct recruitment from any other law school as of now. Mckinsey and Bain do not hire directly from law schools
The people who got in were all rounders who usually had good positions of leadership.
People who got in usually planned in advance to make it work.
It is a feeder to get into top universities (especially for MBAs) or join most big organizations you want.
You don't need an MBA to learn the ropes. You just need to be smart.