The Spanish driver will start the race from 10th position after his car proved too slow to fight for a better position. Alonso finished over 1.3 seconds off pole position.
Team-mate Felipe Massa completed a poor day for Ferrari with 12th place on the grid.
Alonso conceded Ferrari needs to find more pace.
"It's almost the first time I remember that one of us is out of Q3 and the other is 10th," said Alonso. "We have to improve.
"We have to stay calm more than ever now things are not going well, just like when things are going well we don't have to get over-excited."
Alonso admitted his main target for the race was to gather an many points as possible, a goal he labelled as 'sad'.
"We'll try to get as many points as possible," he said. "It's a realistic goal, probably a sad goal, but we need to try to get as many points as possible.
"We have been doing poorly so far, but maybe tomorrow it will be better."
Massa also admitted Ferrari had gone backwards since the previous race.
"I think the car is not working like before," said Massa. "In Montreal the car was quick in the race, and even in qualifying the pace was better than what we have here.
"It was definitely more competitive there, so that's the biggest worry. I hope everything changes tomorrow and we see a competitive car in the race."
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