Dominik Szoboszlai struck an 88th minute winning penalty, earned by Florian Wirtz, to secure an important three points.
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Inter midfielder Piotr Zielinski said at the final whistle: "We're disappointed.
"We had a good game, but we lacked something up front to score a goal."
Fellow midfielder Henrikh Mkhitaryan also stated: "We have to keep our head high, work harder. It wasn't our best game, but let's not forget we played against a top side.
"They also did well, I believe it was a balanced encounter. I did my best to try and help the team."
Meanwhile, Switzerland defender Manuel Akanji added, "It's tough to lose this game. The positive side is if we play like this we win most games."