diff --git a/internal/oci/push.go b/internal/oci/push.go
index 1e2d0f2e95..89a6daf9e5 100644
--- a/internal/oci/push.go
+++ b/internal/oci/push.go
@@ -94,12 +94,15 @@ func DescriptorForEnvFile(path string, content []byte) v1.Descriptor {
 	}
 }
 
-func PushManifest(ctx context.Context, resolver remotes.Resolver, named reference.Named, layers []v1.Descriptor, ociVersion api.OCIVersion) (v1.Descriptor, error) {
+// PushManifest pushes the manifest for a Compose OCI artifact. The returned
+// bool reports whether the push fell back from OCI 1.1 to OCI 1.0; it is
+// only meaningful when err == nil.
+func PushManifest(ctx context.Context, resolver remotes.Resolver, named reference.Named, layers []v1.Descriptor, ociVersion api.OCIVersion) (v1.Descriptor, bool, error) {
 	// Check if we need an extra empty layer for the manifest config
 	if ociVersion == api.OCIVersion1_1 || ociVersion == "" {
 		err := push(ctx, resolver, named, v1.DescriptorEmptyJSON)
 		if err != nil {
-			return v1.Descriptor{}, err
+			return v1.Descriptor{}, false, err
 		}
 	}
 	// prepare to push the manifest by pushing the layers
@@ -107,25 +110,26 @@ func PushManifest(ctx context.Context, resolver remotes.Resolver, named referenc
 	for i := range layers {
 		layerDescriptors[i] = layers[i]
 		if err := push(ctx, resolver, named, layers[i]); err != nil {
-			return v1.Descriptor{}, err
+			return v1.Descriptor{}, false, err
 		}
 	}
 
 	if ociVersion != "" {
 		// if a version was explicitly specified, use it
-		return createAndPushManifest(ctx, resolver, named, layerDescriptors, ociVersion)
+		descriptor, err := createAndPushManifest(ctx, resolver, named, layerDescriptors, ociVersion)
+		return descriptor, false, err
 	}
 
 	// try to push in the OCI 1.1 format but fallback to OCI 1.0 on 4xx errors
-	// (other than auth) since it's most likely the result of the registry not
-	// having support
+	// (other than auth) since it's most likely the result of the registry
+	// rejecting the OCI 1.1 request
 	descriptor, err := createAndPushManifest(ctx, resolver, named, layerDescriptors, api.OCIVersion1_1)
 	var pushErr pusherrors.ErrUnexpectedStatus
 	if errors.As(err, &pushErr) && isNonAuthClientError(pushErr.StatusCode) {
-		// TODO(milas): show a warning here (won't work with logrus)
-		return createAndPushManifest(ctx, resolver, named, layerDescriptors, api.OCIVersion1_0)
+		descriptor, err = createAndPushManifest(ctx, resolver, named, layerDescriptors, api.OCIVersion1_0)
+		return descriptor, true, err
 	}
-	return descriptor, err
+	return descriptor, false, err
 }
 
 func push(ctx context.Context, resolver remotes.Resolver, ref reference.Named, descriptor v1.Descriptor) error {
diff --git a/pkg/compose/publish.go b/pkg/compose/publish.go
index 4f362bef19..6d4380fe93 100644
--- a/pkg/compose/publish.go
+++ b/pkg/compose/publish.go
@@ -91,26 +91,32 @@ func (s *composeService) publish(ctx context.Context, project *types.Project, re
 			fmt.Println(string(indent))
 		}
 	}
+	didFallback := false
 	if !s.dryRun {
-		err = s.pushComposeArtifact(ctx, project, repository, layers, options)
+		didFallback, err = s.pushComposeArtifact(ctx, project, repository, layers, options)
 		if err != nil {
 			return err
 		}
 	}
+	text, status := "published", api.Done
+	if didFallback {
+		text, status = "published (registry rejected OCI 1.1; fell back to OCI 1.0)", api.Warning
+	}
 	s.events.On(api.Resource{
 		ID:     repository,
-		Text:   "published",
-		Status: api.Done,
+		Text:   text,
+		Status: status,
 	})
 	return nil
 }
 
 // pushComposeArtifact pushes the compose artifact manifest to the repository,
-// and the application image index when publishing a full application
-func (s *composeService) pushComposeArtifact(ctx context.Context, project *types.Project, repository string, layers []v1.Descriptor, options api.PublishOptions) error {
+// and the application image index when publishing a full application. The
+// returned bool reports whether the push fell back from OCI 1.1 to OCI 1.0.
+func (s *composeService) pushComposeArtifact(ctx context.Context, project *types.Project, repository string, layers []v1.Descriptor, options api.PublishOptions) (bool, error) {
 	named, err := reference.ParseDockerRef(repository)
 	if err != nil {
-		return err
+		return false, err
 	}
 
 	var insecureRegistries []string
@@ -120,20 +126,20 @@ func (s *composeService) pushComposeArtifact(ctx context.Context, project *types
 
 	resolver := oci.NewResolver(s.configFile(), desktop.ProxyTransportFor(ctx, s.apiClient()), insecureRegistries...)
 
-	descriptor, err := oci.PushManifest(ctx, resolver, named, layers, options.OCIVersion)
+	descriptor, didFallback, err := oci.PushManifest(ctx, resolver, named, layers, options.OCIVersion)
 	if err != nil {
 		s.events.On(api.Resource{
 			ID:     repository,
 			Text:   "publishing",
 			Status: api.Error,
 		})
-		return err
+		return false, err
 	}
 
 	if options.Application {
-		return pushApplicationIndex(ctx, resolver, named, descriptor, project)
+		return didFallback, pushApplicationIndex(ctx, resolver, named, descriptor, project)
 	}
-	return nil
+	return didFallback, nil
 }
 
 // pushApplicationIndex pushes an image index referencing every service image,