Carragher said: "That's a load of rubbish. Of course I want to play. But whoever signs for Liverpool, if they play full back they know they're going to have a fight on their hands to get in the team.
"When we report for pre-season the manager will do what he always does and give everyone a fair crack of the whip to earn a place. I don't expect it to be any different this time."
Carragher also insists that the Reds fifth-placed finish last season was far from the disaster it was painted as by team-mate Steven Gerrard.
Carragher added: "Everyone is entitled to an opinion in this game and we don't always have to agree with each other. I've read Stevie thought the season was 'a disaster'. I know why he's said that because it's a big disappointment not getting in the Champions League.
"It's understandable some of the lads feel that way, but I wouldn't go that far. You can't say the season has been a failure when you've beaten Manchester United to win a trophy.
"At the end it was as if oming fourth would have been a great achievement, but it was only important because of the Champions League.
"If you'd asked me at the start would you rather come fourth and win nothing or come fifth and beat Manchester United in the Worthington Cup final, I'd have taken the winners' medal every time.
"A lot of fans will have their own view on that, which I'd expect, but as a player what you want is medals, not to come fourth.
"I don't think there's a lot of difference between coming fourth and fifth in the league really but it mattered more this season because of the Champions League place.
"Whether we'd finished fourth or fifth, it still wasn't good enough for Liverpool.
"Obviously it's a big blow for us not to be in the Champions League and we'll miss it next year. But with all due respect to the likes of Leeds and Newcastle, who've done well in the competition recently, what have they actually won in comparison to us?
"Leeds reached the semi-final a few years ago but what do they have to show for it now? What we really want is to win the league. That's the real target for us again next season, not just qualifying for Europe."