Norway went ahead midway through the first half when the Hegerberg sisters combined to make the breakthrough.
Andrine Hegerberg sent a free-kick into the box for sibling Ada to head past Siobhan Chamberlain from close range.
England are next in action on Tuesday when they face Sweden, the Olympic silver medallists from Rio, in Murcia.
Their best chances against Norway fell to Fara Williams and Lucy Bronze, who saw efforts from the edge of the box go over the crossbar.
Steph Houghton's shot from a corner was cleared off the line, while Ellen White had a penalty appeal turned down after she appeared to receive a shove in the penalty area.
Norway continued to push for a second goal but Chamberlain made a string of impressive saves to deny the opposition.
With the Women's Super League clubs returning from their close season break only two weeks ago, the majority of the England players are still some way from peak fitness.
Even so, with the European Championship seven months away, a defeat by quality opposition such as Norway will be a disappointment to England manager Mark Sampson.
The match was England's first since November and they appeared to lose some of the free-flowing football they were displaying in the back end of 2016.
Having failed to create a single clear-cut chance in the first half, the introduction of Millie Bright and White looked welcome in the 68th minute.
The team came to life in the closing moments, when they won a string of corners which they followed up with on-target efforts but failed to find the equaliser.
Sampson played a 3-4-3 formation and despite the defeat, England looked mostly solid across the park but lacked the creativity to find an equaliser for large part of the game.
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After topping their Euro 2017 qualifying group, England came into the match on a 10-game unbeaten run and showed a gritty determination to get back into the match.
Chamberlain, deputising for the injured Karen Bardsley, made a string of impressive saves to prevent England from going further behind.
Jade Moore once again showed her battling qualities and her ability to control play in the middle of the field, while on the left wing Demi Stokes displayed pace and power.
For some players, this training camp could be one of their last chances to impress before the summer and Sampson is expected to make a number of changes ahead of Tuesday's match against Sweden.
Striker Danielle Carter, who did not play against Norway, will miss the Sweden game with a hamstring injury.
The Arsenal striker, 23, will remain with the squad in La Manga. Chelsea defender Hannah Blundell has been called up as a replacement.
Match ends, England 0, Norway 1.
Second Half ends, England 0, Norway 1.
Gunhild Herregarden (Norway) wins a free kick in the defensive half.
Foul by Millie Bright (England).
Offside, England. Lucy Bronze tries a through ball, but Nikita Parris is caught offside.
Foul by Elise Thorsnes (Norway).
Nikita Parris (England) wins a free kick on the right wing.
Attempt blocked. Stephanie Houghton (England) header from the centre of the box is blocked.
Corner,  England. Conceded by Nora Holstad Berge.
Corner,  England. Conceded by Nora Holstad Berge.
Attempt blocked. Stephanie Houghton (England) right footed shot from the centre of the box is blocked.
Corner,  England. Conceded by Ingrid Moe Wold.
Foul by Ingvild Isaksen (Norway).
Jo Potter (England) wins a free kick in the defensive half.
Corner,  England. Conceded by Nora Holstad Berge.
Offside, Norway. Maren Mjelde tries a through ball, but Kristine Minde is caught offside.
Attempt missed. Jade Moore (England) right footed shot from outside the box is too high. Assisted by Alex Scott.
Ingrid Moe Wold (Norway) wins a free kick in the defensive half.
Foul by Demi Stokes (England).
Substitution, Norway. Gunhild Herregarden replaces Anja Sonstevold.
Attempt missed. Ellen White (England) right footed shot from outside the box misses to the left. Assisted by Toni Duggan.
Ingvild Isaksen (Norway) wins a free kick in the defensive half.
Foul by Millie Bright (England).
Attempt missed. Toni Duggan (England) right footed shot from the centre of the box is close, but misses to the right. Assisted by Alex Scott with a cross.
Toni Duggan (England) is shown the yellow card.
Nora Holstad Berge (Norway) wins a free kick in the defensive half.
Foul by Toni Duggan (England).
Substitution, Norway. Vilde Risa replaces Andrine Hegerberg.
Substitution, England. Ellen White replaces Fara Williams.
Substitution, England. Millie Bright replaces Jodie Taylor.
Corner,  England. Conceded by Nora Holstad Berge.
Delay over. They are ready to continue.
Delay in match Andrine Hegerberg (Norway) because of an injury.
Corner,  England. Conceded by Andrine Hegerberg.
Nora Holstad Berge (Norway) wins a free kick in the defensive half.
Foul by Jade Moore (England).
Foul by Ingvild Isaksen (Norway).
Fara Williams (England) wins a free kick in the defensive half.
Offside, Norway. Elise Thorsnes tries a through ball, but Lisa-Marie Karlseng Utland is caught offside.
Foul by Karina Saevik (Norway).
England women began their 2017 season with a 1-0 friendly defeat by Norway in Spain, bringing their 10-match unbeaten run to an end.