The hosts went 2-0 up at Pittodrie through Jamie Fowler's own goal and Willo Flood's header but wasted a string of chances to kill the contest as Kilmarnock sub Kris Boyd pulled one back to instead set up a nervy finale.
"First and foremost, getting the three points was the most important
thing," McInnes said. "All week we've been itching to go and agitated to get in amongst it.
"We wanted so badly to get off to a winning start, and I felt there was a push for that from the support, people who work at the club, and the directors.
"We did that, and I thought we did it with a bit of style. We showed enormous passion and energy, and that was transmitted from the crowd as well.
"They were vocal when we needed them to be, and hopefully the 13,000-plus will be there when we play at Pittodrie again.
"We cut them open, and had a lot of good play at times. We've only ourselves to blame for not scoring more. Craig Samson's had a couple of good saves, but none that you would think he shouldn't be making.
"I'm not going to be too critical, but we should have been out of sight by half-time.
"The scoreline made the game sound closer than it was, and if the players can put in that level of performance most weeks, I think we'll be there or thereabouts."
Allan Johnston was disappointed to have suffered defeat in his first competitive match as Killie boss.
"We know we have to improve," he said. "We gave Aberdeen too much space, and they countered on us a few times and created a lot of chances.
"The positive was the second half performance to come back into the game. We got a goal back and were unlucky not to score another one, but we know we have to defend better as a team.
"The goal shows you the quality Kris has. He's not quite match-fit yet but when he is, he'll be a handful for any defender."