The 29-year-old goalkeeper, who was starting just his second game for his country, was carried off on a stretcher after appearing to injure his knee as he landed after diving in a vain attempt to keep out Miroslav's Stoch's 14th-minute opener.
Magpies boss Rafael Benitez will anxiously await news from the Ireland camp ahead of Saturday's crucial trip to fellow relegation candidates Norwich with first-choice keeper Tim Krul already out for the season with a knee ligament injury.
In Elliot's absence, the Republic rallied to take the lead through two penalties in as many minutes, the first converted by Shane Long and the second by James McClean in front of a crowd of 30,217.