The Ivory Coast striker saved his side from a calamitous defeat at the Britannia Stadium with a equalizer in the 33rd minute after Stoke took the lead in the eighth minute.
But that wasn't enough to appease the Blues fans, who were frustrated with the 33-year-old's hesitance in launching the ball into the penalty box as Chelsea searched for a late winner.
And according to the Daily Mirror, Drogba confronted a fan after the match to ask what was his problem and had to be dragged away by Paulo Ferreira.
A Chelsea source was quoted as saying: "Didier wasn't happy at the accusation and wanted to make his point.
"It just shows how much he cares for the club. He knows the fans have the right to their say but he felt it was going over the top, especially with the effort everybody had put in to try to win the game."
Meanwhile, the draw meant Chelsea's slim hopes of defending the Barclays Premier League title were all but extinguished as they now trail leaders Manchester United by 11 points
