A photo of the opening at the bottom of the stem clamping area taken from below will likely show the stem is fully closed. If the stem and bar were compatible, you'd see a gap of a few millimeters. The absence of a gap would mean that the handlebar and stem were designed for two different diameter standards.
Yes, insert a shim. One or two layers of aluminum cut from a soda can should do it. Aluminum works very well as shim material.
First, though, examine the inner and outer surfaces of the stem clamping area. Here's hoping tightening it as much as you did to clamp the undersized bar didn't create any cracks.