Carroll, a former United keeper, fears for Moyes if his old club suffer a lengthy trophy drought.
"It surprised me a bit, the way Manchester United played against us because, for me, they are a team who want to win every game," he told Press Association Sport.
"They haven't changed too many players from the side that won the league, but David Moyes has had a tough start.
"He seems like a nice guy so I hope he does well, but the fans will have to be patient. I just don't know how patient United fans can be because they don't want to do an Arsenal and not win a trophy for that long, or be like Liverpool and go without winning the league for so many years."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball