Not so. Your manage could say, "I don't have hard dollars for you, but I can free up some of your time if you're willing to do some self-training." Or, "I'm told the training budget is zero. What else can I / we do to work on your skills and/or career?"

But a manager that simply says, "No budget. Oh well. Sucks being you." IS failing to fulfill the role of an average manager.