The Pilgrims shocked the visitors by taking the lead in the 78th minute with a stunning strike by Craig Tanner.
But Gillingham, who had beaten Sheffield United 4-0 in their opening league victory, hit back to progress to the second round with late goals from Bradley Dack and Jake Hessenthaler.
The defeat continued Argyle’s poor run in the League Cup and against Gillingham, who have not lost in their last seven matches against the Greens.
But Adams was more than happy with how his team performed against higher league opponents.
He said: “I thought it was probably our best performance since I came here. We created numerous opportunities in the first half and were probably unfortunate to not go in two or three goals up at half-time.
“I thought we counter-attacked well, passed it extremely well, and it was a very good performance. I think that 2-1 to Gillingham is harsh on us, to say the least, but that’s the nature of football.”
Argyle will be back in action at Home Park on Saturday when they entertain Portsmouth.