The Merseyside club crashed to a 3-0 Premier League defeat at Manchester United on Sunday, having been knocked out of the UEFA Champions League by Basel five days earlier.
After an impressive 2013-14 campaign in which they came agonisingly close to being crowned champions of England for the first time since 1990, Brendan Rodgers' side have endured a poor start to 2014-15 and sit 10th in the top flight.
Bournemouth will attempt to inflict more misery on the out-of-sorts Premier League side when the Championship leaders compete in a League Cup quarter-final for the first time.
But defender Toure, who replaced the injured Glen Johnson in the first half at Old Trafford, is backing Rodgers' side to recover from their latest setback and demonstrate that they are not far from turning the corner.
He told Liverpool's official website: "As a team, the most important thing is that we stick together. We will work hard in training and there is another game coming. We'll give 100 per cent to win in the Capital One Cup and we're going to be better.
"It is a very important game for us and we'll give all we have got to win it. Every game is really important for us.
"We can go really far in the Capital One Cup and it's very important to win a trophy."
Bournemouth boss Eddie Howe has worked wonders since returning to Dean Court following a second spell at Burnley and the south-coast club knocked out West Brom to reach the last eight.
Howe is relishing the prospect of facing Rodgers' men and believes criticism of his opposite number has been harsh.
"The game against Liverpool is a really special one in the club's history," Howe told Sky Sports. "We've never been to a major cup quarter-final in our history so to be up against a club the size of Liverpool with their history makes it all the more special for us.
"I think they've been incredibly unlucky. You look at the game against Manchester United on Sunday, I thought they were excellent and on another day I think they would have won the game with all the chances they created.
"People overreact and look very short-term in football. Brendan won manager of the year last year and deservedly so in my opinion and he's still an outstanding manager."
Brad Jones is expected to continue in goal for Liverpool in place of Simon Mignolet, who was dropped at Old Trafford, while Johnson looks set to miss out with a groin problem sustained in Sunday's defeat.
Mario Balotelli will be hoping for a recall to the starting line-up following an encouraging display after replacing Adam Lallana at half-time at the weekend.
Bournemouth are unbeaten in their last 12 matches and Howe must decide whether to start leading scorer Callum Wilson, who has been named among the substitutes in every tie of the club's historic cup run so far.
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