The Reds secured their first victory at Arsenal since February 2000 courtesy Saturday's 2-0 success and the vice captain has challenged his teammates to maintain the high standards they have now set themselves.
"It was a big game for us and a big result," Carragher told liverpoolfc.tv.
"I'm not sure what message it sends out but it may make some people sit up and take notice and think this Liverpool team could maybe do things this season.
"The challenge for us now is to build on this result. This win has put us in a good position."