The Premiership side avoided an upset with a nervy 6-5 victory in a penalty shoot-out after 120 minutes of action finished goalless at Pittodrie.
Jamie Langfield made the decisive save from Michael Doyle, and Mark Reynolds held his nerve to book McInnes' side a place in the next round.
"I need to say that some of our play in the first half was really slick, we moved the ball about well," McInnes said. "The tempo of the game and appetite of the players really knocked Alloa out their stride.
"Alloa are used to enjoying the game, and we didn't let them do that. We didn't get a goal which is a concern and gave Alloa encouragement, but I praise the players for their mentality to see it through.
"The quality of penalties was fantastic for both sides, and their boy was really unlucky."
Alloa boss Paul Hartley added: "When it goes to penalties it can be a lottery at times. All the penalties were good and Langfield makes a great save. Sometimes there's a hero and a villain.
"Overall I thought we were fantastic. We defended well, attacked well and pushed Aberdeen all the way.
"It's another clean sheet, and I thought our three centre-backs were great. We matched Aberdeen all the way, and I was proud of them.
"They've got to keep that going for the rest of the season. It could have been an upset, but it wasn't to be."