The Royals succumbed to two goals in the final 23 minutes as they bowed out of the competition, but despite seeing the Rams create double the number of opportunities, Adkins believes that his team deserved more from the game.
The 49-year-old is quoted by BBC Sport as saying: "Against a team who play excellent possession football, I thought it was us who were in control of the game at that time.
"Unfortunately, the goal changes the complexion. It's a great bit of wing play leading into the second goal which is unfortunately a deflection - the second one in two games now against us."
Reading return to Championship action on Sunday afternoon when they take on Wolverhampton Wanderers.