"Denied the opportunity" is a gross exaggeration, given in most European Union member states the number of foreign-born residents is made up primarily from people born outside the European Union. EU member states are generally regarded as generous when it comes to migration, much to the dismay and consistent criticism of their respective tabloid papers.
I'm also skeptical of your conclusion as to why people voted leave. In case you missed the poll, it wasn't just the 65+ age range that voted this way. Even down to the 25-49 group you're looking at a 45% leave vote. Age distribution isn't equal either - the majority of the UK falls in the 25-64 group band, which varies between voting leave or voting remain depending on which poll you look at.
In what way are they more invested? They have ~5-25 more years left and then it makes no difference to them. Furthermore, they're likely pretty settled in their life and already retired.
Young people are still building their lives, trying to establish their career. They're likely going to be denied the opportunity to live and work in 27 countries. I think it's pretty disgraceful that they've torpedoed our future based on their hazy rose-coloured memories of some supposedly-better past.