Writing to a professor who contributed to my research paper I was working along with a professor on a research paper during my masters in 2014. I graduated in that year but we still worked on the paper for next year.
After that I moved to another city for my job. I could not follow up with the professor regarding the paper and had no contact with him after leaving. Now after 3 years, I received an email from a journal that the manuscript has been submitted by my professor.
I felt really embarrassed that I could not provide inputs for finalizing and submitting the paper.
How should I write an email to my professor to tell him that I am embarrassed for not being able to follow up and would like to contribute in any future modifications for that paper?
Just say it as you have here, I think. It seems perfectly reasonable. It also seems like a good idea to reconnect for future projects. 

But you don't say why you were contacted. Either you were listed as a co-author or were given an acknowledgement. Some journals get permission for all acknowledgements from all parties. It would be good to know beforehand which case it is, and what your feelings are about how the professor included you. 

But you gain nothing, now or in the future, by staying silent.