The Indian ace finished the tournament with nine points and had to be content with fifth place among nine contenders.
Carlsen emerged a clear winner with 18 points under the soccer-like scoring system in place in the tournament.
Kramnik scored 16 points, while Adams ended with 13, alongside Hikaru Nakamura of the United States.
Nakamura was involved in the lone decisive game of the day. The American accounted for Briton Luke McShane.
Judit Polgar drew with Armenian Levon Aronian, who finished on eight points for sixth place, while the Hungarian woman was seventh with six points.
McShane was eighth with five points and Gawain Jones of England [ Images ] finished last with three points coming from three draws.
The new world rankings, to be announced on January 1, will see Carlsen scaling the all-time high rating and the Norwegian will proudly stand at 2861 points.
Carlsen bettered the 2851 rating scored by Garry Kasparov [ Images ].
Kramnik also gained heavily from the tournament and will replace Aronian as the world number two, with 2809 being his new rating.
Anand lost three rating points from the tournament; the Indian ace is now number seven in live but unofficial ratings.
Results, final round: Magnus Carlsen (Nor, 18) drew with V Anand (Ind, 9); Hikaru Nakamura (Usa, 13) beat Luke McShane (Eng, 5); Judit Polgar (Hun, 6) drew with Levon Aronian (Arm, 8); Michael Adams (Eng, 13) drew with Vladimir Kramnik (Rus, 16).