Chris Coleman's side had been on course to challenge the likes of England, Germany, Spain, Italy and France for the inaugural title in European football's third major global competition but lost out by less than 600 coefficient points.
Four group winners from division "A" in June 2019 will determine the victor of the first draw of the League of Nations.
Germany, Portugal, Belgium and Spain are the top seeds and can not play each other, with France, England, Switzerland and Italy in pot 2.
For the UEFA Nations League Finals, the group winners of UEFA Nations League A will play in a knockout format (semi-finals, third-place match and final) in June 2019 to become the UEFA Nations League winners.
Wales have missed out on potentially money-spinning games after failing to make it into League A in the new UEFA Nations League format.
There are four tiers and nations have been placed with teams of similar ability.
Monday's defeat against the Republic of Ireland proved costly in terms of missing a World Cup European Qualifier play-off spot, and it also meant they were leapfrogged by the Netherlands in UEFA coefficient, dropping them out of the top 12.
The competition, which UEFA says will replace most worldwide friendlies, will be played in September, October and November 2018, with a group stage draw scheduled for next January.
The Republic of Ireland are in League B along with Austria, Wales, Russia, Slovakia, Sweden, Ukraine, Bosnia and Herzegovina, Northern Ireland, Denmark, Czech Republic and Turkey.
How does the Uefa Nations League work? .
The draw for individual groups takes place in Lausanne, Switzerland, on January 24, 2018.
Each league will have its own play-off competition with single-leg semi-final and final to decide who gets the final four places.
The tournament will be used to reduce the number of friendly matches across the worldwide calendar and provides four qualification spots to Euro 2020.
After a traditional Euro 2020 qualification determines the first 20 participants, UEFA will use the Nations League tables to determine the last four teams to join them - one from each League.