Niall McGinn scored the only goal at Pittodrie after four minutes, before the Dons squandered several chances to put a gloss on the result.
McInnes said: "I thought we were worthy winners. Jamie Langfield hasn't had a save to make the whole game, but we made it more difficult than it had to be at times.
"We started with a real tempo and a bit of aggression about us. We couldn't have asked for a better start with Niall's finish. You can see why he's been so important to us.
"A real piece of quality won us the game, but we were wasteful and it should have been put to bed long before the 90 minutes were up.
"Kilmarnock, as they do, had plenty of possession of the ball and forced us to put an extra body in the middle of the park.
"But where we're falling short at the moment is putting the ball in the back of the net."