The English Football Association on Monday briefed England players that they could be suspended from the national team if they trigger a major breach of the new code of conduct, which will take effect next month.
"If someone transgresses in a way that brings the integrity of the team or themselves or the organisation into question, we have the ability to warn them, or if we deem it appropriate, under significant circumstances, to suspend them from England," said Club England managing director Adrian Bevington.
"I'm beginning to think it's the most important thing I've got to deal with as chairman," said Bernstein.
A new code is expected to be in place in time for next month's friendly with Sweden in Gothenburg.
FA officials said no fines are being incorporated into the code, although suspensions are authorized. The code is expected to bring some clarity to a complicated disciplinary system.
The FA began the process of drafting a new code in January.
Information from Press Association was used in this report.