Bannister - named the Mets' top minor league pitcher of the year earlier in the day - got off to a shaky start in the first inning, allowing a three-run double to catcher Ariel Pestano.
Cuba tacked on a fourth run in the second inning on Michel Enriquez's RBI double. Run-scoring hits by Juan Carlos Moreno and Carlos Tabares chased the right-hander with one out in the third inning.
Reliever Jason Phillips then allowed a two-run homer to third baseman Yuliesky Gourriel, with Cuba's seventh run being charged to Bannister.
After a standout season in minor league competition, split between Double-A Binghamton and Triple-A Norfolk, Bannister has struggled in World Cup play.
In three starts, Bannister is 1-2 with a 9.69 ERA, having allowed 18 hits and 14 earned runs in 13.0 innings. He has walked five and struck out 10 over that span.
Bannister suffered his second loss of the tournament Wednesday, both of them at The Netherlands' Rotterdam Stadium. On Sept. 9, Bannister allowed six runs in 3-2/3 innings to Nicaragua, an eventual 14-2 defeat.