"I think Liverpool and Tottenham will be vying with Arsenal to get that fourth place," he told Sky Sports News.
"It's not set in stone who will finish up there at the moment and certainly Liverpool have got to run them a lot closer than they did last season or the year before.
"There's no reason why Liverpool or Tottenham can't get in that space because it's so tight between those teams. I certainly expect an improvement from Liverpool this season."
Carragher retired at the end of last season having spent his entire career with Liverpool, making 737 appearances for the club.