The Merseyside club have struggled at Anfield so far this season, drawing seven times already.
Carragher has now said that his side will have to improve their form if they are to continue their push for European qualification.
"It wasn't the result that we wanted but Stoke are a tough nut to crack and they have proved that a lot of times this season," said Carragher.
"They have got a very strong back four and unfortunately we couldn't break them down.
"It's been a problem a few times at Anfield this season.
"We need to sort that out before the end of the season if we want to get to where want to be, which is obviously the top four."
Liverpool travel to Bolton on Saturday for the late kick-off.