The Dons went three down to a Rory McAllister penalty and a double from Jordon Brown, who was released by the Dons this summer, before Barry Robson and Niall McGinn pulled goals back.
McInnes said on the club's official website: "Even although it was a friendly game and we give the players plenty of warning about how they are coming up against a determined team, they did not take notice of those warnings.
"I thought there was a lack of resilience and determination for the three goals we conceded. There was a determination from their boys and credit to Jordon Brown who was excellent throughout. We also did not deal with Rory McAllister in the first half.
"We had a few injuries so we had to reshuffle things and I feel we were a lot better in the second half. I thought we played well and showed more determination but when you give three goals away you are always going to be up against it. It is a worry for me."
Clark Robertson and Russell Anderson were taken off because of injury concerns but McIness revealed they were more precautionary measures than anything serious.
Gregg Wylde, Calvin Zola and Willo Flood missed the game through injury but could be fit for the league opener against Kilmarnock on August 3.