Morgan beat keeper Karen Bardsley after connecting with Lauren Holiday's cross, her 50th international goal.
England were flat before Jodie Taylor had a goal controversially disallowed for offside after Fran Kirby had a shot tipped on to the bar.
The Lionesses launch their World Cup campaign against France on 9 June.
But head coach Mark Sampson knows he has work to do to fine tune his side ahead of the tournament in Canada.
England were lacklustre for long periods before a late rally failed to produce an equaliser in front of a 14,369 crowd.
Sampson takes his players to the Cyprus Cup next month on the back of two straight defeats following the 3-0 setback to Germany, Fifa's top-ranked team, at Wembley in November.
The USA, two-time World Cup winners, arrived in Milton Keynes on the back of a 2-0 defeat by France.
Yet they were rarely troubled and went ahead when Morgan met Holiday's 25th minute cross to nod the visitors into the lead.
England survived a penalty scare when Christen Press goes down under a Jill Scott challenge but the referee awarded a corner instead of a spot kick.
The game's most controversial moment arrived in the 56th minute, Taylor wheeling away in celebration after poking home when Kirby's shot was tipped on to the bar before rebounding back into play.
But the celebrations were cut short by an offside flag, television replays showing the goal should have stood.
Bardsley denied Morgan what would have been a stunning second goal - the USA striker beating Alex Scott inside the box in the 75th minute before being thwarted by a strong save.
England pressed for an equaliser in the closing stages but could find no way through a well-drilled United States defence on a frustrating night for the hosts.
England head coach Mark Sampson: "We scored a goal which is a good goal, so it is always disappointing when the officials let you down.
"It's just a wrong decision. These girls are in pre-season still, so we knew we needed to be resolute. Physically we weren't in a position to compete and we knew we had to be a bit clever.
"Tonight we have learned we can be a threat on the counter attack, which is a huge positive for us because normally we dominate possession."
