The Dons boss admitted his side could have been distracted by the trappings of last Sunday's Scottish League Cup success but felt they dominated the game, despite falling behind to Kris Boyd's 11th minute opener.
He said: "Today, coming back to Pittodrie, the game was all about last Sunday. The fans were celebrating it, the programme was all about last Sunday and the players were seeing people they've not seen since then.
"It could have been difficult but I never felt it would be an issue for them."
Adam Rooney levelled soon after before Ryan Jack stroked home a 72nd-minute winner for the home side.
McInnes added: "The scoreline suggests it was closer than it was. We were the dominant team and were unfortunate to go behind. It was no more than a half-chance, but Kris has stuck it away, so we're disappointed with that.
"The response was almost immediate and I felt we were always going to score goals and win the game. It was pleasing to see that players, and the crowd, weren't getting agitated.
"We constantly asked questions of them, kept the ball well, moved it well. I'm delighted with the attitude of the players."
The Dons are ahead of Motherwell in the race for second place only by virtue of goal difference after the win and McInnes added: "We just want to keep winning and keep the consistency we've been showing. If we can maintain the level of performance we have done so far this season, we'll be there or thereabouts.
"There are some good teams around us but we can only affect ourselves and we'll finish where we deserve to finish."
Kilmarnock boss Allan Johnston felt his side had stopped Aberdeen playing but was frustrated to have thrown away the early lead Boyd's score had given to them.
He said "It's always a difficult place to come and we set out to try and frustrate Aberdeen. We did that for long periods and I don't think there was too much between the teams.
"Aberdeen always looked dangerous on the counter-attack. There were some pleasing things, but it was disappointing to concede the two goals we did.
"When you get in front against a quality team like Aberdeen, you've got to defend well. The second goal came from a free-kick and it's basics like that you have to work on. You can't afford to lose goals in the manner we do.
"You can see the mentality Aberdeen have got. They're used to winning week-in and week-out, and they ground it out."
Although sitting in eighth place in the league, Killie are just three points above the play-off place currently occupied by St Mirren, and Johnston cannot foresee much changing in terms of who finished in what half of the table at the split.
He said: "I think everybody's in it, and anyone can beat anyone. We're where we are because of the number of goals we lose, but we've got a lot of big characters in our team, people who can make a difference. It's all about producing it on the park.
"We have to look after ourselves and get ourselves as far away from trouble as we can. There's a lot of big games between now and the end of the season, and we have to start picking up results."