The Baggies dismissed the 59-year-old on Monday following a torrid run of just two wins from their previous 21 Premier League games, leaving the club close to the relegation zone.
McAuley insists that he enjoyed working with Pulis but recognises that the demands of "modern-day football" mean there is not "an awful lot of time" for a manager to get a side out of trouble.
"We're in a difficult place," McAuley told Sky Sports News. "The club have felt that there may not be a light at the end of the tunnel and they probably felt change was the best way to maybe get a response.
"He was good for me at the football club. I was signing one-year deals and he was keeping me here and he could have moved me on.
"It was good working with him and just the run of form that we've been on and the way it is in modern day football. You don't get an awful lot of time to try turn things around. We've just got to get together and move on from it."
Former Crystal Palace and Newcastle United manager Alan Pardew is believed to be the firm favourite to take over at The Hawthorns.