To be clear, while the amount of the tip you leave is somewhat flexible, in countries like the United States where it is customary, you should leave a tip unless the service is extraordinarily bad (but that's been so rare that when it happens I complain to the manager and get the entire meal comped.)
Not leaving a tip actually punishes the waiters and staff, since many restaurants typically underpay the hourly for waiters and instead expect them to make it up from tips. Plus, many restaurants share tips between waiters, as well as with the busboys and sometimes even the kitchen staff, in order to encourage cooperation.
We can argue that this is an unreasonable or an unfair system, but I think that's off-topic. The point is that tipping is expected behavior and it's fairly rude not to add the tip to the cost of the meal. I'm sure there are many customs in their own country that would be similarly impolite if ignored.
That being said: If someone has offered to pay for your meal, and does not leave a tip, it's on them, not on you. You should try to explain the custom to them, but you should neither force them to leave a tip or risk embarrassing them by ostentatiously leaving a tip where they can see you doing it.
If you want, you can make some excuse to separate yourself from the group on your way out, go to your waiter (or the manager), and surreptitiously give them some cash, with a brief explanation:
I'm sorry, my friends are from Europe where they don't tip, so I hope this will cover it? Thank you so much for a wonderful meal!
If you can pull this off, you will have gracefully smoothed over any ruffled feathers from the restaurant staff while simultaneously not ruffling any of your friends' feathers, the best of both worlds.
If not, then let it go for now -- but make sure to remember the name of your waiter.1 The next time you visit, you should be able to request that person, and leave them an extra tip to make up for the previous visit.
1. I can't speak for other places, but in every restaurant in California that I know we have the same primary waiter the entire meal. The exception is when one waiter is done for the day, in which case they come over to explain and introduce the new waiter. The other people who come around to clear dishes or refill drinks are other staff like busboys, etc, which is why I mention that many restaurants share tips, to motivate everyone to provide the best service. This is for restaurants that have formal waitstaff, of course.