Hamren: Sweden are winners, despite exit
"My philosophy as a coach is that if you behave like a winner, you're going to be a winner. Sometimes it takes time because of the circumstances, but you're going to be a winner," he told a news conference.
"For me the players have been winners, even when we lost."
With no chance of qualifying for the last eight following defeats by Ukraine and England, the Swedes came out determined to show that they had deserved their place in the competition.
Zlatan Ibrahimovic scored a stunning scissor-kick to put the Swedes ahead early in the second half and Sebastian Larsson scored a late second to stun the French, who limped through to the quarter-finals behind group winners England.
"The difference today from the two games against England and Ukraine was that the margins were more on our side defensively," Hamren added.
"France had some good chances, the difference today compared to England and Ukraine was that France didn't score from those chances they had.
"I'm glad that we won this match and I'm proud of the players, but it hurts too."
The coach introduced Christian Wilhelmsson at halftime and the winger had an immediate effect on the game with his electric pace and trickery, leaving many to wonder why he had not started.
"You always think about that - could I do something else, would it have been better with someone else?" said Hamren, adding that he was still considering the best way to use Wilhelmsson for the upcoming World Cup qualifiers.
"You never know if it's going to be better, but of course I've been thinking about that and I'm going to think about it the whole summer."
Captain Ibrahimovic was given the man of the match award.
"The prize is not just for me, it's for the whole team. They give me the freedom to play the way I can play, without them I can't do anything," he said.
"Today we had a nice ending, we said this morning we wanted to finish in a good way. We have had a lot of supporters here and we wanted to do it for them."