Co-hosts Ukraine came back from a goal down to win their Group D opener 2-1 on Monday with two headed goals from talismanic striker Andriy Shevchenko.
Sweden have now conceded five headed goals in their last three games, including three from corners.
A defeat on Friday in their second game will scupper the Swedes and England coach Roy Hodgson and burly striker Andy Carroll will have noticed Sweden's weakness in the air.
Despite their poor record, Hamren was philosophical.
"It's a part of football, you can't do so much about it," he told reporters after the match.
"With the corner, we should have won it in the first area with Zlatan [Ibrahimovic], we had a man on the front post but not in the spot we wanted. Sometimes it happens."
Rather than focus on his side's defensive failings, Hamren praised Ukraine hero Shevchenko's predatory instincts.
"He was really good in the box, two really good goals. That made the result. Good for him, bad for us," he said.
HUNG UP
After conceding three goals in recent friendlies against Iceland and Serbia - all headers, two from corners - Hamren said his side would not get "hung up" on their defensive frailties.
"We can do that the day we lose," Hamren had told a news conference in the lead-up to the Ukraine game.
That day has now arrived and if Sweden want to progress they will have to address their defensive frailty.
Their zonal marking system at set-pieces has been a complete failure, with players unsure who to pick up and when to do so, resulting in free headers for the opposition from corners.
Seasoned defender Olof Mellberg is still able to deal with high balls into the area from deep but his defending of crosses when facing his own goal has let Sweden down in the last few games.
A serious knee injury sustained by Daniel Majstorovic forced Hamren to reshuffle his pack, and Andreas Granqvist has not looked entirely comfortable alongside Mellberg at the back.
OLSSON OPTION
Waiting in the wings is Jonas Olsson.
At six feet four (193 cm) the West Bromwich Albion centre-back has the height and experience of English football needed to deal with England's potential aerial threat.
Having played few games at club level due to injury, Celtic full-back Michael Lustig found it hard to keep pace and left the gap at the near post for Shevchenko's sublime second goal.
Granqvist has been impressive at right back in recent friendlies and he could move from the centre of defence to replace Lustig with Olsson coming into the middle.
Hamren's team selection gambles may not have paid off against Ukraine but he is nothing if not courageous.
"Only five or six players reached the level I wanted tonight.
