Authenticating gitlab-runner docker container running on CI server

I receive this error when using the image: in my .gitlab-ci.ymlwhich points to an image on my private gitlab docker container registry.

ERROR: Build failed: API error (500): Get https://gitlab.example.com:4567/v2/main/example-image/manifests/latest: error parsing HTTP 403 response body: no error details found in HTTP response body: "{\"message\":\"forbidden\",\"status\":\"error\",\"http_status\":403}"

This build is being ran in a docker executor, however, that docker executor, obviously, is not authenticated with the gitlab container registry. I have successfully docker logined in my CI server, however, I am not able to docker login in the gitlab-runner container running on that same CI server because docker is not installed on that image.

Am I doing something wrong or is it not possible to use your private gitlab container registry in a docker executor?