Frank Lampard was also called away at the last moment and Grant believes that may have had an effect on his side's performance.
Drogba will have a scan on his injured knee on Tuesday to assess the damage but Grant was unable to say whether either player will be available for Thursday's clash with Everton.
"It is a personal matter with Frank and I would prefer to leave it at that," said Grant.
"I didn't like the first half but I think the players were a bit in shock because one of our best players had to leave the team at the last moment, which is understandable.
"Didier will have a scan tomorrow and we will see. We will wait and see with Frank as well."