How did you select your polygons before Eliminate was run?

You could do a Select by Location using "Are completely within" to get polygons enclosed by another class. https://desktop.arcgis.com/en/arcmap/10.3/map/working-with-layers/using-select-by-location.htm

With the selection you could then run the eliminate to only get rid of those contained sliver polygons. https://desktop.arcgis.com/en/arcmap/10.3/tools/data-management-toolbox/eliminate.htm

You could try the following:

Run Multipart to Singlepart. https://desktop.arcgis.com/en/arcmap/10.3/tools/data-management-toolbox/multipart-to-singlepart.htm

Select by Location using "Are completely within" to get polygons completely within another. https://desktop.arcgis.com/en/arcmap/10.3/map/working-with-layers/using-select-by-location.htm

With the selection run Eliminate to only get rid of those contained sliver polygons. https://desktop.arcgis.com/en/arcmap/10.3/tools/data-management-toolbox/eliminate.htm