Paul Hembery was unhappy after some teams opted to ignore Pirelli's pre-Indian GP tyre directive to limit the number of laps on each set.
Ahead of Sunday's race at the Buddh International circuit, Pirelli told the teams "not to use the soft tyre for more than 15 laps and the medium for no more than 35 laps" based on safety grounds.
But, according to the BBC, the FIA refused to "order the teams to follow the advice" meaning they were free to do what they wanted.
Two teams notably did that with both Lotus and Force India running marathon stints to great success and double points finishes.
In fact Romain Grosjean even achieved a podium result after 46 laps on the medium tyres.
Hembery, though, was not happy.
"We are disappointed to see that some teams went against our recommendations and used the compounds for longer than we advised them to do," said the Pirelli motorsport director.
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