I don't think you are doing anything wrong. I have seen before manuals suggesting removing the foot, but th eonly time it has worked for me was for beading with a high end Bernina. I tried with my singer and it didn't work. Is your Singer a low shank or a slanted needle? I am sure you can get a darning or embroidery foot for it. A darning foot for a slanted needle is harder to come around, but it does exist.
Maria
I did some research and found that it is slanted needle. If you have a Singer store nearby they can locate one for you.