The Reds were eliminated from all three knockout competitions they entered in 2012-13 as Rodgers coped with having a small and inexperienced squad.
Seven academy players were drafted in for debuts during the campaign — though the boss was able to add proven talent with the signings of Philippe Coutinho and Daniel Sturridge in January.
Their arrival was a factor in an upturn in form during the second half of the campaign, and Rodgers hopes similar success in the transfer market over the coming months will enable Liverpool to challenge on all fronts.
“This time, we’ll certainly give the League Cup and the FA Cup a proper go — we have a much better squad to do that,” he said. “We had a paper-thin squad last year, we had kids all the way through. Obviously those players who have come in have added quality and it’s no coincidence that we have kicked on when we’ve had quality in the group.
“We need to improve the group and the depth but that’s what gives me great hope for the summer. If we can add that, we can make a real start and then we’re ready to challenge.”
Rodgers has already secured a deal in principle to bring Manchester City’s Kolo Toure to Anfield, helping to fill the void left by retiring defender Jamie Carragher.
On the potential make-up of his squad when the 2013-14 season kicks off, he added: “You can flip it about, but it’s the depth really. We just need to build up the depth of the squad.
“I want to have people who might be disappointed because they’re not even on the bench. At the minute we probably don’t have that so it’s competition we want to get.
“I don’t want a massive group, we want a tight group with a real core of 17 or 18 players who feel they should always be playing and then supported by a few of our top young talents.”