How to reconcile with an old mentor after (unintentional) plagiarism accusations The question is not about plagiarism, it is about its aftermath. I am presenting the whole situstion.

Three years back, in my undergraduate years (summer after sophomore, to be precise), I did  my first major project with a professor in India. The project came out well and we had two publications next year. 

Obviously happy with my work, the professor offered me another project, next year, which was entirely different and of higher level of difficulty (he had his graduate student working on it). He asked me to do simple simulations and mostly literature survey so that he could later use it. He also proposed some survey papers (all by same author, call him X) to start with. I wrote the survey section based on the papers mentioned in the citations by X, and added reviews of another dozens of paper. I cited all survey papers by X and cited others too. I also did certain simulations.

Meanwhile, he provided me references to land into a Masters program at one of the top 5 electrical engineering programs in the USA, and I will be forever indebted to him. After I came to USA, he had his graduate student worked upon the project and submitted a paper (I was surprised to be listed as co-author) including the survey section and simulations I did an year ago. 

One of the reviewers pointed that the survey section has been almost a replica of X's works. The reviewer added that, although X's works has been cited, word plagiarism is still relevant. I got disappointed and wrote my mentor and email apologizing for letting him down. He didn't reply.

Now, it's been six months since the review came, and I really wish to reconcile with him. What can I do ?

few clarifications

The plagiarism was using 3-4 sentences from various papers without double quotes but properly cited. Also, half of my citations were same as X's works. It happened because, my survey was about major techniques in a field while X's surveys were about techniques in a subfield of the field.

I emailed the professor only once. He didn't reply and I never emailed him again.

I never knew how my section was going to be used because the project-work was incomplete. When his graduate student finished the work, he immediately submitted the paper and informed me after the submission. I should have got time to review something I did an year back.
Nobody is going to mention that the OP's old mentor put undergraduate work directly into a publication (i) without checking that it met professional-level standards of academic honesty and (ii) without informing the undergraduate that this was being done or that he was being added as a coauthor?  In my view, these transgressions are equally bad or a bit worse than including a few sentences without quotation marks from sources that have been cited in a survey paper.  

In my opinion there is a good chance that the mentor is embarrassed that these lapses of his own have been exposed, which complicates the OP's situation.  I am surprised that other answers seem determined to pin this all on the OP.  @Scott Seidman suggests that the OP contact the editor:


  I think an email to the editor involved, cc'ed to your mentor, taking responsibility (without qualifiers) and stating that none of the other authors were in a position to recognize or correct this prior submission,


In my view the mentor was in the position to recognize and correct academic cultural errors made by his undergraduate mentee, and since the OP was not involved in the preparation or submission of the manuscript in any way, the responsibility for this clearly lies at least partially (and I would argue, primarily) with the mentor.  Sending such an email to the editor could just call attention to his poor mentorship and supervision: i.e., it could actually make it worse.  (Pro tip: don't contact an editor about something unless you're sure all your coauthors are on board.  If there is any real doubt, clear it with them explicitly.  If someone is not returning your emails, you can't do this.)

The OP is not blameless in the situation: he made a mistake, and a mistake involving what sounds like a borderline instance of academic dishonesty.  He should apologize to his old mentor -- which he has done -- and move on.  I would recommend that the OP continue to treat his mentor like an old mentor: i.e., send him occasional emails keeping him up to date on his current academic life.  I would certainly not assume that someone never wants to hear from me again based on a single unanswered email.  But ultimately the mentor should know that he made mistakes as well, from a position of far more experience and responsibility.  It does not fall on the OP to take any kind of heroic or (especially) self-abnegating measures to remedy the situation.  One hopes that eventually these two people can move past one negative interaction amid many other good ones.