The Finn stayed in the pits in the closing minutes of the first qualifying session at the Hungaroring on Saturday, with the team believing he had done enough to secure his progression on the medium tyre.
However, Marussia's Jules Bianchi subsequently eclipsed his time to leave Raikkonen out at the first hurdle and facing an uphill battle for points in Sunday's race, as he starts from 17th on the grid.
The 2007 world champion failed to make the top 10 in qualifying for the third successive race, despite his Ferrari looking quick enough to challenge team-mate Fernando Alonso in fifth.
The 34-year-old revealed after the session that there had been discussions on whether to return to the track, insisting his team were confident he was safe with a time of one minute 26.792 seconds.
"The plan was to go out, but the team said 'No, you are fine, you do not need to go out'," Raikkonen said. "I questioned it a few times, but they said no need, and we can see the end result.
"A mistake has been made. It's already been a difficult year, so I don't see the point to shout. The mistake is done.
"People make mistakes, but there are things we have to change to improve.
"As a team in Formula One, as Ferrari, we should not be doing these kind of things. None of us are in our first year. These are not easy times.
"Obviously we have to improve, to do things differently. We can see there are weaknesses in the system. That's how it goes."
This latest blow for Raikkonen caps a poor return to Ferrari that has seen him finish no higher than seventh in 10 races, and score a mere 19 points.