The 54-year-old was delighted with how his side performed in the 2-0 victory over Les Bleus, but admitted that he was sad to leave the team's hotel in Kiev
And the former Rosenborg boss was particularly pleased with his rearguard after Blagult claimed an impressive 2-0 victory over France in their final group game.
"We performed badly in the first half against Ukraine, but we have been good in two games and we need to remember that the difference was that today, we had the margins with us defensively.
"France had some really great opportunities, like England and Ukraine, but France were not able to score with the opportunities that they had.
"We had some really good saves from our goalkeeper and some of their chances went wide of the goal; there was a header at the end which was dangerous.
"But I'm really happy about how we performed in these games and really happy that we won this game. I'm really proud of the players, but at the same time, it's a bit painful right now, it hurt. I think we're all a bit sad after this game."
The 54-year-old had been criticised recently for leaving Christian Wilhelmsson on the bench, but claimed that his detractors are talking with the benefit of hindsight.
"I said earlier this week, when you've already played the game you think about the result. Could I have done something else? Would it have worked better with someone else? Or playing some other way tactically?
"They are the questions when you don't have the result [ahead of you], but it's easier after a game to know than before. Also, you never know if it's going to be better if we had done that [play Wilhelmsson], but of course I have been thinking about that."
Hamren also admitted that he is saddened to leave the team's base in Ukraine.
"We have really liked our stay in Kiev, [it was a] fantastic hotel, fantastic people working there and it was like leaving a friend today when we left the hotel.
"So for them too it was a great game, [as well as] for us and our supporters because I think they feel happiness and they share it with us, but we're disappointed we're leaving, but that's life," he concluded.