City manager Mark Hughes targeted the Burkina Faso international on Friday and opened talks concerning a loan deal with a view to a permanent switch in the summer.
However, the move broke down and on Monday Pitroipa explained to L'Equipe that his current club were the ones to blame.
"Contrary to what has been said, it was not due to my agent that I didn't join Stoke," he said.
"It was due to intermediaries appointed by Rennes on that case."
The 27-year-old has made 20 Ligue 1 appearances so far this season but is yet to find the net, and he was not included in the matchday squad for Sunday's 2-0 home win over Lyon.
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