Steven Gerrard's Ibrox side Glasgow Rangers were beaten in their last outing.
Rangers went into their game against the Dons in good form, but they slipped up at Ibrox.
Rangers were unable to get past Aberdeen, who played with 10 men for a large chunk of the game.
And McAuley claims that Rangers defence were very frustrated with the way that they conceded.
The towering centre-back said: “They won a lot of free-kicks in the first half, put a lot of balls into the box and scored off one of them. We were disappointed we didn’t defend that better, although McKenna finished it well, to be fair.
“That’s disappointing for me personally and for the other defenders. That’s why we are looking at our own performance as our downfall. We were sitting in the dressing room looking at ourselves after the game. Our standards dropped individually and as a team. We let ourselves down all over the park from where we have been this season. That’s why we lost the game.”
Rangers had a chance to build on their lead at the top of the Scottish Premiership table had they beaten Aberdeen.
However, their defeat allowed Celtic to close the gap and Kilmarnock to overtake them.
Rangers are next in action at the weekend when they take on Dundee, as they look to get back to winning ways.