Two second-half goals from Liam Kelly prove the difference at the Madejski Stadium.
Ady Pennock said he was pleased with the performance of his players despite being eliminated from the Carabao Cup on Tuesday evening.
Gills were defeated 2-0 on the night but had chances to take the lead, particularly through Tom Eaves who forced a fine save before Reading's first goal.
After the game Pennock said: "Obviously we are disappointed with the defeat but I thought we gave a good account of ourselves. In the first half we had two or three half chances and then just before they scored we had a great chance and their keeper pulled off a very good save from Tom Eaves.
“The lad [Kelly] then scored a worldie to be fair to break the deadlock but we’ve come here and had a good go. We were playing against a very good team and we gave a couple of debuts to the young lads which I was really pleased with.
“With Greg Cundle he was making his debut, Ben Chapman come off the bench for his debut so I’m pleased. I’m disappointed because we lost but I thought we had a good go.
“You’ve got to give Reading credit and I want to wish them all the best in the next round. It’s a great stadium to come to, hopefully the young boys get a lot out of this because they deserve their starts and we look forward to Saturday now."