The Swedes crashed out of Euro 2012 in the first round, and in France they managed a lucky draw against Ireland before losing to Italy and Belgium, which again sees them depart early.
"One point in three matches is something I'm obviously not happy with, but we deserved more," Hamren told reporters at the team's final news conference of Euro 2016 before revealing his plans for the near future.
"I feel strongly for a break. If something turns up that is impossible to say no to it might be different. I've turned down some offers," he said.
Hamren announced before the competition that he would be stepping down to be replaced by former IFK Norrkoping coach Jan Andersson, who led his underdog side to the Swedish title in 2015.
From the high of the playoff victory to the disappointment of another early departure, a shaken Hamren said he will now take stock of what happened.
"I'm going home to Sweden to bury myself for a while. It's going to be tough, I feel that already," he said.
"I'm going to need some love and understanding from those closest to me, as I'm not going to be too pleasant for a while."
After a disastrous first half in the opening game against Ireland, the Swedes gradually improved but it was too little, too late, and the defeat to Belgium consigned them to the bottom of the group, leaving Hamren to depart on a low note.
"I have really appreciated my time as national team coach. I have loved having the honour, the benefit of leading our national team for six and a half years," he said.
Also leaving the international scene are goalkeeper Andreas Isaksson, midfielder Kim Kallstrom and record goalscorer Zlatan Ibrahimovic.
"I'm proud to have worked with the greatest player in the history of Swedish football," Hamren told reporters as he summed up his time at the helm.
"I think we have done something very good together, even if I wish it could have been even better."
(Editing by Julien Pretot)
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