Liverpool's Carragher concentrates on top spot
"There are other teams who could get into the top four this year - but hopefully not at our expense," he told the club's official website.
"We're not thinking about that, though, we're just thinking about the title and not about fourth place.
"A couple of teams have jumped out so far," noted Carragher.
"We've already played Tottenham and Aston Villa and of course Manchester City are the side a lot of people are talking about, but if we start playing the way we can then I'm sure we'll be right up there.
"We've only played four games and if we go on to have a successful season then we'll play more than 60 matches, so it's a long season and there's still a long way to go."
"We've not had the best of starts but hopefully we'll soon start coming into our own," the 31-year-old added.
"We've got Burnley up next and they've been a great story so far, beating two of last year's top five in Manchester United and Everton. Owen Coyle has done a great job with them so we know it's going to be a difficult game."