Shaqiri's wonderful volley had earlier cancelled out a drilled opener from Jakub Blaszczykowski, but Granit Xhaka's penalty miss was pivotal as Poland won the shoot-out 5-4.
Many of Poland's players ran to the Switzerland end of the stadium to celebrate their win, which Shaqiri criticised when he spoke to the media after the match.
"I don't know what to say," said Shaqiri.
"They are professional players - they should know they have to go to the other side to celebrate. What can I say?"
Shaqiri's acrobatic strike is a certain contender for the best goal of the tournament, but the Stoke City midfielder said his "beautiful" finish was little consolation after his team exited the tournament.
"You don't know me so well - I've scored loads of nice goals!" Shaqiri joked when asked if he considered the goal to be the best of his career.
"It was a very important goal and was more important for me because it pushed the team and the fans on. Of course, it was beautiful.
"But in the end we are out and I'm disappointed."
Shaqiri suggested that Xhaka will recover quickly from his miss, blasting the ball well wide from 12 yards, and insisted he was "proud" of his team-mates despite their defeat, which he compared to their extra-time loss to Argentina at the 2014 World Cup.
"I think Granit is very professional, he can cope with it," Shaqiri said. "That's football, everyone can make mistakes.
"Sometimes you're the best, sometimes you're the saddest. That's what you have to cope with. Granit will stand up again and continue. I hope he will score in the round of 16 at the World Cup.
"What can I say about this? We're disappointed. We could have achieved something very big. We have to learn from that. We had the same situation against Argentina.
"We're all proud of our effort. We're proud of playing like this in the tournament. We would have deserved to advance. That's football in the end. The penalties are 50-50."