"If you want someone to take responsibility, then it's me, if you wanted to hang someone, hang me," a tired Hamren told a news conference at Sweden's team hotel, a day after a 3-2 defeat by England ended their interest in the competition.
Sweden, who lost their tournament opener to Ukraine, face France in their final Group D game on Tuesday, but cannot qualify for the knockout stage.
"A good first half yesterday and what was in my eyes a very good second half, and still we lost 3-2. I said yesterday that the margins weren't on our side, offensively or defensively, and they weren't with us yesterday or against Ukraine," Hamren said.
Hamren has won praise for playing a more expansive style than his predecessor Lars Lagerback, but has also been heavily criticised for poor defensive performances and puzzling team selections.
But he pointed to his achievements in club football with Denmark's Aalborg and Norway club Rosenborg and said it took time to affect change.
"We have something exciting on the go with players who have a different way of playing to the way we played previously. There is hope for Swedish football," he said.
"You never know if you'll get the chance to keep working. I hope to get the time and possibility to do it."
Hamren's job is not considered to be under threat, despite his side falling short of their stated goal of qualifying for the quarter-finals.
"I said that we could have three good performances without going on from the group. We have two defeats and no chance of qualifying," added Hamren, who pointed to "one bad half, one ok half and two very good halves" his team had played.
Coaching at his first major tournament, Hamren said Sweden had not reached the necessary skill levels.
"Good teams, really good teams, they get the margins, they make them for themselves. And they do it because they are skilful, and we are not there yet. We haven't reached that level."
Despite having stayed up most of the night reviewing Sweden's games at Euro 2012, an obviously exhausted Hamren said he was ready to start planning for the future.
Whether or not all his players will keep playing remains to be seen, with Swedish media reporting that Anders Svensson and Olof Mellberg are set to quit the national side, but Hamren said neither had spoken to him about their plans.
