The Grove squad has had a rough opening four races to the year, as it is unable to compete with the rest of the pack due to the uncompetitiveness of the FW42.
In Baku, FP1 was cancelled after Russell ran over a loose drain hole cover which caused heavy damage to the car, while teammate Robert Kubica crashed in qualifying.
It put mounting pressure on the struggling British team, who has been lacking spare parts so far this season.
"It was as good as could be really,” said Russell after crossing the line in 15th.
“We knew coming into this weekend that it would probably be the hardest weekend of the year for us.
“Put that on top of myself being really ill since the start of last week, and then Friday with the manhole cover ruining the whole of Friday and the guys having to work all day and through the night to get the car fixed.
"I am quite relieved that this weekend is over, it didn’t seem like anything was going our way. Moving on to the next race, we are still pushing and hopefully Barcelona will be more positive."
Kubica started the Grand Prix from the pit lane after he crashed heavily into the barrier at Turn 8.
The Pole finished behind teammate Russell, admitting he was having trouble with the car for the race, but thanked his mechanics nonetheless for the job they did to repair his car.
"I have never raced here in Baku and would like to say thank you to the mechanics.
"They did an amazing job to get the car back into one piece due to my mistake. We decided to start from the pitlane and very soon it was clear that I had to be careful under braking.
"It wasn’t easy, but the priority today was to bring the car home and I achieved this. Once again thank you to the mechanics as they achieved something extraordinary to get the car on track for the race."
Bahrain International Circuit - Winter testing