The Baggies recorded their first victory at Anfield 45 years to the day since their last thanks to Peter Odemwingie's 75th-minute strike - his 11th of the season.
"We're absolutely delighted and there's no hiding that," a jubilant McAuley told the WBA website.
"It has been a long time since the club's got a win here. We rode our luck at times and we're thankful to the post and crossbar. We had to put our bodies on the line and that's part and parcel of getting a result here.
"It adds to the fun of it because we've managed to ride our luck and come out of the game with a great win.
"There were a few times today when all we could do was look at each other and smile because we got away with some things. But maybe you earn that over the course of a season.
"Today our goal was certainly charmed and we're grateful for that. It's a great win and we'll enjoy it."