The Blues lost 1-0 to Middlesbrough in the first leg of their Carabao Cup but it could have been different had Palmer put his shooting boots on.
Minutes after Hayden Hackney gave Boro the lead at the Riverside Stadium, Palmer had the chance to score an equaliser.
Enzo Fernandez's speculative shot was spilt by Tom Glover with Palmer lurking but his effort was smashed over the bar from about five yards out.
Speaking on talkSPORT, ex-Premier League striker Dean Ashton was shellshocked.
He said: "He is one talented player but this is an absolute disaster, a shocker.
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"It bounces straight to Palmer five yards out and he puts it over, that's pretty unacceptable.
"You can't miss that, sorry at this level it's unacceptable."
Moments before Boro took the lead, Palmer had the first of his golden chances when he intercepted Jonny Howson's poor backpass.
But instead of tucking home, his shot flashed wide when he had both corners to pick, making it a tough half for the 21-year-old.
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Palmer had another chance before half-time to atone for his errors after a fine piece of work to chop back onto his left-foot.
But his shot was weak and easily saved - to the jeers of the home fans.
The England Under-21 international had been asked to lead the line by Mauricio Pochettino on Tuesday night.
Nicolas Jackson has jetted off to the AFCON with Senegal while Armando Broja was left on the bench.
While the Albanian eventually did come on, Chelsea still posed little threat despite dominating the ball and Boro took home the win.
If Michael Carrick's men avoid defeat in the return leg on January 23 at Stamford Bridge, they will reach the Carabao Cup final in a massive shock.