Hamren was asked about possible England concerns that the Swedes, eliminated from the tournament, would field a weakened side in their last Group D match against France.
"Make sure you win yourselves," he advised England. "That's the best thing. They can concentrate on themselves and we'll concentrate on our own game. Our ambition is to get a good performance and a good result."
Hamren added that the Swedes could be even more dangerous to France, level with England on four points at the top of the group, now that the pressure was off.
"We can go out and perform with everything to win and nothing to lose," he told a news conference.
Hamren will rest forward Johan Elmander, who will be given time to continue his recovery from a broken foot.
Hamren said the decision was taken with the player and out of his respect for his club Galatasaray, while midfielder Rasmus Elm is ill and a decision on his fitness will be taken on the day of the game.
Hamren said he and his players were eager to give their fans a good send-off as they head home and he begins preparations for World Cup qualifiers.
"It's the last game, and if we win tomorrow we don't have three points in the World Cup but we have a lot of feelings and self-confidence when we start the World Cup qualification," he said.
Midfielder Kim Kallstrom praised the Swedish fans.
"It's a big tournament, we've waited and prepared for it, so for us it's about finishing the job and starting to prepare for the World Cup qualifiers.
"The support we've had from Swedish supporters has been fantastic and there'll surely be lots there again tomorrow, it's a great source of motivation. We're here to play, even if we can't go through."
Hamren confirmed that defender Olof Mellberg would start against the French but his future in the national team is unclear.
"I have spoken to him about it and he has said that this is his last tournament, but that doesn't mean he won't play a part in the qualifiers," Hamren said. We'll see what happens."
