Teddy Talk: Creating, Collecting, Connecting

I hope someone can help me I  am struggling to get these sew in eyes flush with the face without creating a big hole. As a consequence the eyes are not in very tight and can be pulled out as per my picture. I do secure them by tying the threads together so they wont come completely out but I would like to know how to get them so they don't move at all. I usually use safety eyes but prefer the look of sew in ones.

Any tips would be much appreciated.

Thanks