The Reds face Championship side Blackburn at Ewood Park in a quarter-final replay on Wednesday, with Aston Villa awaiting the winners in the last four.
And Liverpool go into the game in the midst of a mini-crisis, a 2-1 home loss to Manchester United having been followed by Saturday???s 4-1 thrashing at Arsenal.
Having almost won the title last season, the Reds look unlikely to even reach the top four this term, but Rodgers thinks Cup glory would salvage the campaign.
“It’s important to have a game quickly when you lose,” he said.
“The group is very committed to winning this trophy but, in order to do that you have to qualify, and we know Blackburn will be a difficult game for us.
“A trophy this season will mark another step forward for us. Getting to a final and winning a trophy is what we want.
“In terms of the FA Cup, that was always an objective.
“On Wednesday we’ll look to reach our second semi-final of the season in the cup competitions (having been narrowly beaten by Chelsea over two legs in the last four of the Capital One Cup).”
???Blackburn have got some excellent players. They defended well when they came to Anfield (in the original tie, which finished 0-0).
“We’ll go there really focused and determined. We can’t wait to play again after the weekend’s disappointment.???
The Reds went on a 13-match unbeaten Premier League run from mid-December but it has been suggested that recent results indicate that teams have worked out to cope with Rodgers??? preferred 3-4-2-1 formation.
But the manager thinks it is a more a case of a dip in form from his side, who have not been creating as many scoring opportunities as they managed during the unbeaten run.
“I don’t think it’s about being worked out,??? he said. ???We didn’t start well (on Saturday), and it doesn’t matter what system you are playing if that happens.
“In the last four games we haven’t created as much, and that’s more on ourselves.
“Of course you give opponents credit but every team will go into a game to defend well and work hard against you.
“Probably the Blackburn game when we drew 0-0 and the games following that we haven’t created as much.
“That’s something that we want to reinforce, the creativity for chances and hopefully taking those chances.
“It’s a difficult system to play against, but it’s one of a number of systems we’ve played here and played very well.
“It’s my job to always look to find the solutions, that’s what I’ve tried to do in the games when we didn’t look like scoring.”