arcobjects - Spatial relationships that do not match

All, I have 2 layers as shown below

What I want to do is go through each feature (in pink) and do a spatial filter against the green layer. My current code is

        inMemFeatCur = inMemFeatClass.Search(null, true);
        inMemFeature = inMemFeatCur.NextFeature();
        while (inMemFeature != null)
        {
            //set the spatial filter
            ISpatialFilter spaFil = new SpatialFilterClass();
            spaFil.Geometry = inMemFeature.Shape;

            spaFil.GeometryField = validationLayer.ShapeFieldName;
            spaFil.SpatialRel = esriSpatialRelEnum.esriSpatialRelIntersects;
            spaFil.SpatialRelDescription = "";

            //query the results from the spatial filter

            IFeatureCursor geomCursor = inMemFeatClass.Search(spaFil, true);

The problem is the when I go through the geomCursor, it will not find the polygon that is completely outside.

The check i want to do is each polygon (pink) completely within (common boundaries allowed) the green layer. If it is not, a warning will to appear.

I know that IRelationalOperator returns a bool, but i have to go through each green feature which I don't want to do, as I'll be looping many times for each pink feature.

Has anyone got any ideas on how to do this.