"The Big Chucker"
I could find under the criteria first stated was Michael Jordan, going for 40 points against Golden State while only shooting 11-30 (36.7%, though he was 18-19 from the line) in a loss during the 1986 season. Kobe went 17-47 (36%, 7-7 FT) during a 2002 loss to Boston, though he scored 41 points. Kobe also went 13-37 (35.1%, 15-19 FT) in a 2005 loss to Memphis, finishing with 45 points.
Allen Iverson's worst shooting 40 point game seems to be a 2002 game where he went 13-36 (36.1%, 14-16 FT), though the 6ers beat the Pacers. Paul Pierce also had a relatively poor shooting night in Boston's 2003 play-off match-up with the Pacers, though he put up 40 on 8-24 (33.3%, amazing 21-21 FT to make up for it) and the Celts won. So, unless this was a college game or just a question you wanted to know the answer to for kicks, Pierce is the fewest FG's and lowest % I could find over 40. Though, his team did win.
BTW, basketball-reference.com, you rule:
If a player shot 8-27 and dropped 40 points in a loss which NBA player would it most likely be?