Alonso heads into the race only two points behind championship leader Lewis Hamilton, who starts second, but has resigned himself to slipping back.
"It's sad but we're not fast enough. Our expectations were high - the car's potential has increased," he said.
"The podium is out of reach and with Hamilton on the front row it's easy to expect we will lose ground to him."
In the second part of qualifying, Alonso was only 0.218 seconds slower than the fastest car,
Romain Grosjean's Lotus,
but there were nine cars in between them.
Alonso admitted he would have made it through into the top 10 shoot-out had he used two new sets of the faster 'soft' tyres instead of the conventional strategy of doing a first 'sighter' run on the slower 'medium' tyre.
It was a plan adopted by Red Bull's Sebastian Vettel, who ended up on pole position and is just one point behind Alonso in the championship.
Inside F1 - European GP qualifying
"It's easy to say now that with two runs on softs in Q2 we would have made the cut," he said, "but maybe now we would be here lamenting the fact that we did not have two for Q3: it's always easy to judge things after the fact.
"However, we were not quick enough to be in the top 10 in the second part of qualifying and now the race will naturally be tougher."
He added: "We missed a little bit of top speed maybe because we were a little bit slow on the straights.
"We were only 0.2secs off pole position so performance-wise it was one of the best qualifying sessions of the season for us, [but] in terms of position it was one of the worst, so very tricky."
Alonso said he was hopeful he could make up ground in the race as he is starting on the grippier side of the track and has more sets of fresh tyres available than those in the top 10.
Tyre conservation is expected to be critical in the high temperatures expected for race day.
"The race will be very long and will be run in even higher temperatures, which means everyone will have to be very careful when it comes to tyre management," Alonso said.
"Let's hope that, starting from the clean side of the track I can quickly make up a few places and then we will try to also make the most of the two sets of new 'softs' we have left: that's at least a small consolation after this far from positive afternoon."
The result was a surprise to Ferrari, who have made a big step forward in performance after a poor start to the season and have been fighting for victory in the last three races.
It was especially bad timing for the team because Ferrari president Luca di Montezemolo was making a rare visit to a race and was in the garage for qualifying.
Di Montezemolo said: "Just a few thousandths of a second is all it took to prevent Fernando and Felipe from making it through to Q3 and it's a real shame, because looking at the times in the final part of qualifying and the potential of our car, we could have been in the fight for the rows right at the front.
"I am very disappointed, because I was hoping for something better: the positions on the starting grid definitely don't reflect the worth of today's Ferrari and on top of that, it has happened at a track where it is particularly difficult to overtake."
European Grand Prix 2012, day three
Sunday, 24 June: Race 12:10 BST; BBC One and BBC One HD, BBC Sport website and BBC Radio 5 live. Race highlights 22:30-23:30; BBC Two.
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