The 29-year-old delivered an inch-perfect corner kick at the start of the second-half, which Breel Embolo expertly connected with to leave Wales trailing in the contest.
Shaqiri was one of the more impressive performers in a closely contested affair and could be considered unlucky to have been withdrawn from proceedings in the 66th minute.
Wales coach Rob Page said, “We knew Switzerland were going to have a lot of the ball so we had to be solid and well-organised defensively and I thought we did that in the first-half.
“We said at half-time we were doing the right things defensively.
“Shaqiri was causing us a few problems with the counter-movement, where he was going in behind and the centre-forward was dropping in - which we dealt with."
Former Wales boss Mark Hughes was also in agreement with Page and suggested that Shaqiri's exiting the field of play influenced the final scoreline.
"I thought that the Shaqiri substitution changed the game in our favour. Once he went off, we got on the ball a lot more," he said.
"Switzerland just recognised the weakness we had in the middle of the box and they had the quality of delivery [for the goal]."