Oli Shaw scored a brace in what was the Dingwall club's first victory at the Global Energy Stadium since their opening-day triumph over Motherwell. Charlie Lakin and Jermaine Hylton were also on target, while Aberdeen got on the scoresheet thanks to an Alex Iacovitti own goal.
The defeat means that the Dons cede third place to Hibs, while County move off the bottom of the league.
McInnes said: "We have lost three players to injury and the biggest concern is Jonny Hayes and Ross McCrorie are leaving the ground on crutches," he said.
"Ash has also suffered a problem with his back.
"The opening period of the game, to go behind in less than 40 seconds wasn't good enough.
"It gives the team at the bottom of the league real encouragement and their front three caused us problems.
"For us not to be scoring more from the chances created is disappointing."
Conversely, County boss John Hughes was delighted with his team’s display and the fact it took Shaw less than a minute to open the scoring.
"Getting off to a fantastic start certainly helped us – and that's something we've been looking for,” said Hughes.
"Somebody mentioned our home record and I hadn't realised it was as poor in the league.
"But I have said we need to make this a fortress and start picking up results.
"Tactically, I felt we got it spot on, with the three attackers, who had plenty of pace in them.
"We gambled, we sucked it in and hit on the counter and we played it over the top of them and it worked for us a treat.
"These players have good legs in them and I'm really pleased."
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