World Cup winner France is under pressure ahead of Monday night's must-win home game against Croatia, which won 1-0 at Denmark thanks to Mario Pasalic's close-range effort midway through the second half.
The Danes top Group 1 with six points, while Austria and Croatia have four.
``We didn't win, we'll take this point and try to win on Monday,'' Mbappe said. ''You should never be anxious, you should just try to improve.''
Mbappe, who has recovered from a blow to his knee, latched onto a pass from fellow substitute Christopher Nkunku to sprint clear and curl a left-footed shot into the top corner in the 83rd minute for his 27th international goal at the age of just 23.
Four minutes later, Mbappe hit the crossbar after combining with Karim Benzema and Nkunku. France finished strongly with midfielder Matteo Guendouzi having an injury-time effort saved by goalkeeper Patrick Pentz.
``We had so many chances in the second half. We had the control of the game but we weren't efficient enough,'' coach Didier Deschamps said. ``These aren't the results we expected. But obviously we're not in our best form.''
France looked fragile in the first half, and fell behind when striker Andreas Weimann put former Manchester United interim coach Ralf Rangnick's side ahead in the 37th minute.
Liverpool's Ibrahima Konate made his France debut in the center of defense. But he was far too static on Austria's goal, as Marko Arnautovic sent Konrad Laimer skipping on the overlap down the right and his cross was swept in by Weimann.
Karim Benzema, who scored minutes into his international debut against Austria in 2007, earlier had a close-range header superbly saved by Pentz.
Pentz then kept out Benzema's curler and a shot from Benjamin Pavard as Les Bleus hit back.
Mbappe came on in the 63rd for the ineffective Antoine Griezmann, who has not scored for Atletico Madrid or France since early January.
Only the group winners make it to the Final Four, while the last-placed teams will be relegated. The group winners in the lower leagues will gain promotion.
In the second-tier League B, Manor Solomon scored twice in the second half as Israel rallied to win 2-1 in Albania to lead Group 2.
Armando Broja's penalty gave the Albanians the lead in first-half injury time, but Shakhtar Donetsk winger Solomon replied with a superb run and shot from the left flank. He clipped the winner in from close range after a cross came in from the right.
In League C, Kazakhstan drew 1-1 in Belarus and leads Group 3 by one point ahead of Slovakia. Winger Vladimir Weiss scored Slovakia's late winner in a 1-0 win at Azerbaijan
In League D, Group 1 leader Latvia has nine points after winning 4-2 at second-place Moldova for its third straight win.
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