Make the old customers part of a 'legacy' tier which allows them to continue to pay the same and receive the same, but don't allow new customers to join that. Put new customers in the 'fancy shmancy' tier and allow old customers to migrate there (with price increase) for whatever new features you are adding.
It's still going to be a bitter pill for the old customers, but it IS better than saying "Sorry, you gotsa pay more now! Suckers!"
If you run a subscription-based web app and you determine that you need to increase your prices, what's the best way to do it?
Grandfathering existing customers obviously makes sense, but what if that's not an option? What if you need to charge them more to survive?