How badly will a master's thesis plagiarism report affect my career? This is a question continuation of this post: How to defend plagiarism in master's thesis. I want to thank all the people who helped me in the last post with their answers.
In the academic committee, I admitted that I made a mistake but it was unintentional. I was not given a chance to correct my errors but I presumed it because in private universities, they actually have many restrictions and I was sad because I knew that unknowingly I did a bad mistake. I learnt my lesson. I got my master's degree by clearing exams and without taking credit of the master's thesis.
My university dean informed me that they will keep this in the University record and they will release it if some graduate school and government officials ask about me to the university. I have the chance to appeal against it. Personally, I feel that there is no good that. I got a good PhD opportunity in the USA as I had an MSc from India and I am doing my research there. I want some suggestions:

Do you think that I should appeal?
If I don't appeal, I will get my MA degree from the previous university in the USA anyway. Should I submit my MA degree certificates and result to any other US universities in future in post-doc or for any job?
How drastically will this incident affect my research career in the future?
Any answer will be opinion-based, so here is my opinion.
If you already got into a PhD program, just move on and focus on your current research. The odds are your upcoming contributions will be the key documents defining your career for the years to come. A master thesis, in my opinion, won't be really examined by anyone. Yes, sometimes you find a truly outstanding master thesis, but usually it is just a mildly original compilation made by a fledgling specialist, written with a sole purpose to prove that its author deserves a degree.
In your case the plagiarism you mentioned does not touch the core contribution. Too bad you copied some text verbatim without using quotation marks and endnotes. However, it doesn't invalidate your results, which are the main basis of your degree.
If you feel really scrupulous, I'd advise republishing the &quot;corrected&quot; version of the thesis -- at least, put it on arXiv. Probably, you have other flaws here and there, and if you believe your thesis is worthy, it might deserve a certain minor makeover. Just do it without much delay, and if someone ever questions your thesis, you'd be able to point out that there is a newer version long available, and there is little reason to peruse earlier texts.
A side note: your fault was overlooked both by your supervisor and the referees. It happens.