Alonso had looked like being Sebastian Vettel's main challenger for victory at Sakhir, but his race was wrecked by a DRS failure that meant his wing flap would not close after being activated.
The problem meant he had to stop in the pits twice, once when the issue came to light the first time, and again shortly after when he tried to use DRS once more.
Sunday's result left Alonso 30 points behind Vettel in the championship, but Ferrari team principal Stefano Domenicali believes there is more than enough time to close that gap.
"The gap is 30 points now, but if he has zero points next time and we win, it will be five," explained Domenicali.
"With only four races gone, there is plenty of time. Don't forget, we had a 50 points [advantage] last summer, so it is easy stuff."
Domenicali suggests that Vettel's performance in Bahrain was flattered by the way he was able to control his speed at the front, allowing him to manage his tyre life.
"Sebastian did a very good race, but he was alone and was able to control the pace," said Domenicali.
"We know that when you have this kind of situation, you manage the tyres the best. We saw that in the last race on our side.
"Fernando would have done a very good race, so we need to make sure that in the future we don't have these kinds of situations."
With the DRS failure in Bahrain coming so soon after Ferrari mistakenly left Alonso out on track with a broken wing in Malaysia, Domenicali knows that his team has not made the most of its opportunities this year.
However, he reckoned it best Ferrari did not rue the errors it had made, and instead made sure it gets matters sorted for the rest of the season.
"It's a shame and in this moment it is better to keep the heads up and not to cry too much," he said.
"The biggest things are not positives. We have less points than we should have if you put in place the real performance of the car.
"We could have been always on the podium, and we could have added another win. That's the situation.
"I am sure that the positives will come back and the negatives we had on our side maybe will affect the others soon.
"We need to stay focused. The championship is so long and there is no use to cry too much."