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 told 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 McInnes revealed they were more precautionary measures than anything serious.