can be used to describe a loss of competition by a narrow margin, such as, "he had a narrow miss and didn't make it into the national team".
On another note, "nearly miss" is not the same as "narrowly miss". When you say "nearly miss", it means it actually doesn't miss. For example "I nearly missed my train today" means " I didn't miss the train, but I would have missed it if I had been a few more minutes late". But when you say "narrowly miss", it means it actually does miss. For example: " The bullet came straight to us and narrowly missed me by a few inches" means it did miss me.
On another note, "nearly miss" is not the same as "narrowly miss". When you say "nearly miss", it means it actually doesn't miss. For example "I nearly missed my train today" means " I didn't miss the train, but I would have missed it if I had been a few more minutes late". But when you say "narrowly miss", it means it actually does miss. For example: " The bullet came straight to us and narrowly missed me by a few inches" means it did miss me.