For the second game in a row Hamren's side threw away a lead, allowing an England side inspired by substitute Theo Walcott to recover from 2-1 down midway through the second half.
"I'm very proud of the players," the coach told a news conference, adding that he as coach bore the lion's share of the responsibility for the early exit.
"For the first goal we have to admire England, because that's what they set out to do, use Carroll's game," he added.
"The second goal, we block and we're in the right place but I think it touched Sebastian [Larsson] and changed direction. With the third goal, we had England on the rack and I think they could play the rest of their lives without scoring another one."
Hamren rejected suggestions that Zlatan Ibrahimovic had too much influence in picking the team, and gave credit to forward Johan Elmander, who ran tirelessly despite suffering a broken foot less than five weeks ago.
"I'm the coach, and I pick the team. Of course I talk to my captain, but if Johan had not been injured before the championship he would be playing, but he wasn't ready. Mentally he wasn't ready."
"In football, it's both the feet and the brain. Today Elmander he showed he had the mental strength to do the job."
After a shaky performance against Ukraine, Olof Mellberg put in a towering performance for Sweden, forcing Glen Johnson into conceding an own goal before heading the Swedes in front.
"I think we're sad after today, especially the way we went out, felt we deserved more," Mellberg said.
"We did better compared to the first game, but obviously conceding five goals in two games is really disappointing, without conceding too many chances. You can't afford that."
