Explain why EU residents living in the UK had no vote in the Brexit referendum.

I as an Irish national was permitted a vote (the exception among EU states) and feel that the exclusion of other EU nationals is a form of discrimination, intended or not. Is their opinion not part of the national sentiment?

The franchise for the referendum was debated when Parliament considered the EU referendum bill. For example, you can read the House of Commons second reading debate on the Hansard website: https://hansard.digiminster.com/commons/2015-06-09/debates/15060939000001/EuropeanUnionReferendumBill

You can find all the information and debates on the bill web page: http://services.parliament.uk/bills/2015-16/europeanunionreferendum.html