France romped into a 4-0 halftime lead in the last of the quarter-finals and though the Icelanders showed commendable spirit to fight back after the break another shock after their victory over England never looked likely.
"The first half looked like the playoff second leg against Croatia for the (2014) World Cup. We didn't handle it well mentally," Lagerback said in reference to that 2-0 Zagreb defeat after a goalless first leg.
"It's some kind of mental thing that happened to the players. We weren't using our brains, we didn't play our normal way.
"Part of it is that France were very good but we weren't sharp enough in our decision-making. We made some silly mistakes, and we didn't do well as a team," added Lagerback, who is now handing over the reins completely to current partner Heimir Hallgrímsson after four-and-a-half years.
"It's really impressive that the players turned it around as they did and I don't think it was because France let us do that.
"They showed a bit of the real Icelandic attitude in the second half."
However, Lagerback was full of pride and praise for the way the players had performed through the month, when they won one and drew two group games before shocking England in Nice.
"It's been a fantastic tournament so it's a big thank you to everyone," said the former Sweden coach.
"It's been a fantastic journey for me. I've enjoyed -- maybe not the first 45 minutes today -- but all my time in Iceland and it's been a privilege to be involved. "If you look at the whole tournament, and to reach the quarter-finals, it's been fantastic."
Captain Aron Gunnarsson said the team had been determined to not go out on the wrong end of a thrashing.
"The first half was terrible but the second half we played better," he said. "We decided we couldn't leave the competition like that and I think we saved face.
"We're disappointed but still incredibly proud. It's been such an amazing experience.
"It's been a lot of hard of work and the supporters have been fantastic. They're still singing, it's just unbelievable."
