The Dons were knocked out of Europa League qualifying 3-2 on aggregate on Thursday night following a hard-fought tie against Kairat Almaty.
Even though there were a few tired legs towards the end of the Premiership match, the hosts were in control against Killie, with goals from Graeme Shinnie and an Adam Rooney penalty sealing their victory.
“In the last 15 minutes our natural intensity wasn’t there,” McInnes said.
“A few of the boys started to feel the demands of the games they’ve been playing, but up until then the intensity and intent was there. I can’t praise them enough for that.
“Thursday was important to us but we were looking for a big effort to get the job done today, and it was a real dominant performance in the first half.”
Aberdeen had already requested a postponement of their midweek fixture against Hamilton, which had been scheduled for August 12, and McInnes believes that break will still be beneficial despite their European exit.
“We took the decision while we were still in Europe in order to give us a breath,” he said.
“But it’s still worthwhile in that it helps us win this today, because we’ve asked the players for a big effort and then they have a couple of days off.
“The players have earned a rest. We’ve not really had a chance to take a breath since the middle of June and I can’t praise them enough for having six points from six, with both leagues games coming after demanding European games.”
McInnes was also pleased to see summer signing Shinnie get off the mark for his new club.
“The goal, when it came, it was worth the wait,” he said. “It was a great finish from Graeme. He’s not scored too many in his career but I’m hoping he scores a few more in an Aberdeen shirt.”
Gary Locke’s Kilmarnock side have now lost their first two Premiership games of the new season, conceding six goals without reply along the way.
Things do not get easier for Locke as his side now face champions Celtic on Wednesday night. However, the former Hearts boss retains a level of optimism.
“We finished today’s game in a positive manner and we’ve got to take that into Wednesday,” Locke said.
“It’s been a tough start and we have to go into the game against Celtic with confidence and belief in ourselves, to try to make sure we get the win that we’re needing.
“Today was difficult for us. Coming off the back of last week we set up to be a bit more solid, but it was disappointing that we didn’t get enough bodies forward to support Kris Boyd in the first half.
“I thought when Greg Kiltie came on we looked a lot more positive, very lively. We have to take our chances when they come.”
Goalkeeper Jamie MacDonald pulled off a number of important saves to ensure the scoreline remained respectable, and Locke added: “He had too many saves in the first half, but I’ve brought him in here knowing he’s a good goalkeeper and he’s kept us in the game today.”