After 10 games, the Reds sit third in the table on level points with second-place Chelsea and five adrift of leaders Arsenal.
The Merseyside outfit had a chance to leapfrog the Gunners into top spot, but succumbed to a 2-0 defeat at the Emirates last Saturday.
"They've had a great start," Carragher told the club's official website. "I think the management and the players will all be delighted with the way they've started.
"It was a disappointing result at Arsenal, but they've got Fulham next and you'd expect them to win that game. Arsenal have got to go to United, so someone is going to lose points, so you'd expect Liverpool to be even closer to the top after the weekend."
Carragher retired from playing at the end of last season.