The Gills allowed the 22-year-old to join up with the squad last Wednesday, despite him being out since August because of knee ligament damage.
However, his treatment continued while he was there and the club did not expect him to play in the match.
Hessenthaler was then left fuming after discovering that Sidibe played from the start.
The Gills boss revealed: "We are very disappointed that Mali have pressured Mamady into playing when we knew he wasn't fit.
"I shall be writing to the Mali FA in the next couple of days and protesting in the strongest possible terms.
"What they did in pressuring him to play was totally out of order," Hessenthaler told the club's official website.