Shu claims Tianjin had lined up moves for Spain international Costa, 28, and fellow forwards Karim Benzema, Radamel Falcao and Edinson Cavani.
But Chinese clubs will only be able to field three foreign players per game when the new season starts.
“This situation has brought a change to our signing plans,” said Shu.
Clubs could previously select four foreign players of any nationality and one Asian player in a matchday squad.
From the start of the new season, in March, they must name two Chinese players aged under 23 in their matchday squads, with at least one in the starting XI.
Shu said Tianjin would have made a “big investment” this year had the previous rule remained in place.
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