New screen with no adhesive on the top

Hi,

This is a fairly elementary question but here goes... I replaced a Galaxy S4 lcd assembly and the adhesive was supplied on the back of the part. Everything is fine except I'm not satisfied with the top of the phone around the earpiece as it is not stuck down properly, likely because the included adhesive didn't go up that far. There's really not a lot of room there to use 3m double-sided adhesive and I really don't want to give the phone back to the guy when the top is not secure. I also am hoping to avoid having to dismantle the whole phone and undo all of my work. Does anybody have any ideas as to how I could get this sealed? I can get a fingernail in, so as much as I hate to use the word, super glue comes to mind. Any help is appreciated.