Dexter Blackstock's goal separated the two sides at Highbury as a number of O'Driscoll's summer signings made their debuts.
"Many people would have looked at this tie and looked at it as one of those games that could produce a shock," said the Reds boss after the game.
"But we always looked solid and showed some versatility and that was pleasing. They put us under a bit of pressure in the first half but we changed things round a bit after the break and that seemed to help us.
"We got the goal and had a couple of half chances but to give them great credit they kept battling and we couldn't get the second goal we needed to kill them off. The result went to us but the plaudits go Fleetwood because they were excellent."