So far Kenny Dalglish has brought in England Under-21 midfielder Jordan Henderson from Sunderland.
But having seen Ipswich target Connor Wickham join the Black Cats and Arsenal full-back Gael Clichy apparently set for a move to Manchester City - coupled with arch-rivals Manchester United spending £50million-plus on Phil Jones, Ashley Young and David De Gea - there was a growing feeling among fans that the club were falling behind in the transfer market.
However, Carragher is unconcerned and backed the club's hierarchy, with owners Fenway Sports Group making it clear to director of football Damien Comolli they want to get more value for money from their signings, to bring in the right players.
"It's still very early and I didn't expect too much to happen on the transfer front before now," he told the Liverpool Echo.
"Over the summer players, managers, chief executives and owners are all away on holiday.
"It's only the start of July and with pre-season getting going next week I'm sure things will soon start moving.
"You often find that one deal sets it off and everything happens from there.
"I'm sure it will kick off over the next few weeks and hopefully we'll get a couple more new faces in.
"The club now has a policy of focusing attention on young players and I think that's the right way for clubs to go.
"You want to develop a team and have players at the club for a long time. I think that approach will really benefit us.
"Things don't always work out, but it's much easier to move on a younger player who still has a decent sell-on value than someone in their 30s."
Carragher pointed to the acquisition of Henderson as an example.
"Jordan is a great signing. I know one of the coaches at Sunderland who rates Jordan very highly," he added.
"He had a great season with Sunderland and we're fortunate to have got him. I think he will add real energy to our midfield."