EU President Donald Tusk on Tuesday rebuffed a call by British lawmakers to put the status of Europeans in the UK and Britons living elsewhere in the EU on the agenda of the next EU summit in December.
"I had hoped -- would hope that this is an issue that we can look at at an early stage of the negotiations," May told parliament, saying it was "right that we want to give reassurance" to expatriates.
She added: "But I think the reaction that we've seen shows why it was absolutely right for us not to... give away the guarantee for rights of EU citizens here in the UK, because as we've seen that would have left UK citizens in Europe high and dry."
May has refused to guarantee the rights of an estimated three million EU citizens living in Britain after Brexit until a reciprocal deal is struck for British expats.
She has said however that she wants an "early" deal and raised the issue at numerous meetings with EU leaders, most recently with the Polish premier on Monday.
Media reports had indicated she was seeking some kind of agreement at next month's EU summit, a position cited by more than 80 lawmakers who wrote to Tusk last week.
The apparent failure of May's diplomacy is a "wake-up call" as to how tough Brexit negotiations will be as Britain depends on the goodwill of the 27 other member states, the Financial Times said.
Tusk said discussing the issue at the summit would effectively mean opening formal Brexit negotiations next month -- something only London can do.
EU leaders have repeatedly said there cannot be any talks on Brexit until Britain begins the formal exit process by triggering Article 50 of the EU's Lisbon treaty.
May says she will do this by the end of March.