The Brit’s Renault Sport car suffered a misfire on the way to the grid and the issue worsened until his retirement at the end of lap seven.
That came after the Southwater-based driver was ruled out of qualifying due to an engine fire after just four laps of practice on Saturday morning - forcing him to start from the back of the grid.
It leaves the under-pressure driver without a point this season and rumoured to be fighting for his future with the French team, who endured a tough weekend all-round.
Team-mate Nico Hülkenberg was running as high as fifth in what was a highly-eventful race, however he clipped the wall and broke his front right suspension on lap 25.
That was three laps after the race - which saw three safety cars and numerous crashes - was red flagged due to debris on the track.
The race was won by Red Bull’s Daniel Ricciardo as Lewis Hamilton, who had led for plenty of the day, was forced to make an emergency pit stop to refit his loose head restraint.
That would have handed the advantage to Championship leader Sebastian Vettel, but he was handed a ten-second stop-go penalty for swerving into Hamilton’s Mercedes as they prepared for a restart at the end of one of three safety car periods in Baku.
Hamilton ended up finishing fifth, a place behind Ferrari’s Vettel, and lost two points to the German.
Palmer said: “I experienced a misfire on the way to the grid; it got worse and ultimately the drivability was so poor that we had no choice but to retire the car.
“I made a decent start and then some overtakes into P15 so the start of my race was okay.
“It’s just been one of those weekends; I can’t remember ever having so few laps over a race weekend.
“My hope is to head to Austria with a reliable car so I can have a clean Grand Prix to show what I can do.”
Cyril Abiteboul, Renault managing director, said: “On a day like today, a double DNF is the worst that can happen to the team both in terms of race results and in terms of championship position.
“We need to understand and immediately address the technical issues that prevented Jolyon to even participate, and Nico to start higher in the grid this weekend.
“We saw a highly unusual and eventful Grand Prix today and we will do all we can to make sure that this will be our only double DNF of the season.”