The Italian team were left searching for answers after failing to score a single point in the opening race of the championship for the first time since the South African Grand Prix in 1992.
Kimi Raikkonen, the 2007 champion, crashed into a wall three laps from the end while his Brazilian team mate Felipe Massa, last year’s championship runner-up, retired 13 laps from the finish with a broken front wing.
"This was definitely not a start worthy of Ferrari," team boss Stefano Domenicali said.
"To sum up, it was a day to forget."
Ferrari knew their chances of winning the race were a forlorn hope long before Sunday so decided to pin their hopes on strategy rather than outright speed.
Both drivers started the race on soft tyres in the hope that they would gain an early advantage over their rivals using harder compounds, which take longer to heat up.
But the plan blew up when their softer tyres started to wear after just five laps and, when they came in to the pits early to change, they got stuck behind the safety car.
"I got off to a great start but the soft tyres were a problem," Massa said.
"We had to come in much earlier than we were supposed to… and then it completely destroyed my strategy when the safety car came out straight away.
"It was a very bad to start the season."
Raikkonen said he was experiencing trouble with the car’s grip after switching to hard tyres but only had himself to blame for crashing late in the race.
"I hit the wall quite hard," the Finn said.
"I just suddenly lost the rear end. It is tricky with those tyres but it was probably my mistake."