Songfacts®:

• Elvis Costello composed this song especially for the British-American romantic drama Film Stars Don't Die in Liverpool. The movie is about Peter Turner's relationship with eccentric Hollywood actress Gloria Grahame in the last years of her life.
• Costello explained the song to The Independent:
  
  "'You Shouldn't Look At Me That Way' is a song dealing with two people who have a lot of secrets. They were in a relationship and perhaps had difficulty seeing each other as they really were.
  
  All lovers have secrets. One lover has some vanity but also a lot of vulnerability. The title really came from that. It could refer to a seductive gaze but also a plea not to be judged."
• Elvis Costello told Billboard the story of the song:
  
  "The title really came from the way in which the looks between the lovers kept shifting from Gloria's first encounter with Peter, which was kind of flirtatious. She's quite coy.
  
  The most telling sequence is when she disrobes in front of him in a very matter-of-fact way and it happens to be when she says she's going to audition for the [Royal Shakespeare Company] for Juliet, and he says, 'Juliet? Don't you mean the Nurse?' and she puts the sweater back on in one move. Her demeanor totally changes.
  
  He has to tell her his sexual history too. All along the way things are being revealed. It's easy to overcomplicate these things and ennoble them as if you were very wise, but I'm just saying as a songwriter, these are all great clues as to how to write the song."