The match in Berlin saw Poland battle hard but succumb to their better organized opponents.
The only goal for Poland came from striker Krzysztof Piątek in the 30th minute.
The Austrian team scored goals through Gernot Trauner, Christoph Baumgartner and Marko Arnautović.
Poland are ranked 26th worldwide by football's governing body FIFA, while Austria are No. 25 in the FIFA table.
The Poles were looking to make their mark at the European championships after a disappointing Euro 2020 campaign.
Poland lost 1-2 to the Netherlands in their opening group-stage fixture on June 16.
The championships, held by the European football governing body UEFA, opened on June 14 and run until July 14 in 10 cities in Germany.
Poland boss Michał Probierz said ahead of the tournament that his team was aiming to advance to the knockout stages of Euro 2024 and "will do everything to make that happen."
After facing off against Austria on Friday, the Poles will play France in their final Euro 2024 group-stage fixture on June 25, a do-or-die clash that the Polish team needs to win to prolong its chances of staying in the tournament.
Poland failed to get past the group stage at the postponed Euro 2020 tournament, where they suffered a defeat to Slovakia before drawing with Spain and losing the decisive game against Sweden.
The Polish team made it through to the quarterfinals of the Euro 2016 championships in France, losing to Portugal on penalties.
Poland reached the last 16 of the 2022 World Cup in Qatar before being eliminated by eventual runners-up France.
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Source: TVP Sport, IAR, PAP