Jens Keller's Schalke needed to beat strugglers Nuremberg on the final day of the Bundesliga season to clinch third spot ahead of Bayer Leverkusen and they did courtesy of a 4-1 rout at Veltins-Arena on Saturday.
The result, which condemned to Nuremberg to relegation, saw Schalke finish three points clear of Leverkusen, who edged Werder Bremen 2-1.
Meyer, who was named in Germany's FIFA World Cup squad alongside team-mates Benedikt Howedes, Julian Draxler and Leon Goretzka, says Saturday's triumph proved Schalke can perform when it matters most.
"The pressure's always been there this season," the 18-year-old said.
"We had to get a result against Nuremberg, but it wasn't any different against SC Freiburg the week before.
"We've proved often enough that we can handle this type of situation, now we're just delighted to have defended third place and qualified for the Champions League."
Schalke, who were eliminated by Real Madrid in the round of 16 this season, will be present in Europe's premier club competition once again, having qualified via the play-offs last campaign after placing fourth behind Leverkusen.
Meanwhile, Schalke team-mate Kevin-Prince Boateng believes the German outfit can be proud of their achievements this season.
"It's been a great season and deserve to finish third," said the Ghanaian.
"We had our fair share of setbacks, but always managed to bounce back. Our aim has been to challenge near the top of the league, and we've managed to do that this season.
"We want to do the same again next year."
