Dhoni, instead, questioned umpires in the second Test. He said umpires get "handsome payments" and they were suppose to take right decisions.
There was controversy over Bairstow's dismissal at Wankhede Stadium as Gambhir had taken the catch at silly point after the ball had hit his helmet grille. Umpires failed to spot that and Bairstow walked off during third day's play on Sunday.
However, during the lunch break, England's director of coach, Andy Flower asked Dhoni whether he would reconsider the appeal and call back Bairstow. India skipper said no to it.
Dhoni said: "Is it only my job to recall everybody or will the umpires also do something? (On many occasions), there are replays that show the batsman is lbw. Why can't the opposition say, ‘no my batsman is out, you come back (to the dressing room)?' Umpires get handsome payments, they are supposed to take some (correct) decisions."
During India-England series last year, Dhoni and his team had called back Ian Bell after a controversial run out just before tea time. The Indian team was praised for their move.
This time around, Dhoni did not want to do the same and blamed the umpires, Aleem Dar (Pakistan) and Tony Hill (New Zealand).
There were few decisions which the umpires got wrong during the Mumbai Test which was won by England on the fourth day (November 26).
The third India-England Test begins in Kolkata on December 5.