The Toffees await the semi-final draw following Liverpool’s clash against Southampton this evening after cruising to a 2-0 win over Aitor Karanka's high-flying Middlesbrough side on Tuesday night.
Manchester City and Stoke are the other two sides already through, meaning that the semi-finals will be a top-flight affair.
Everton are yet to win a trophy since 1995, but some fans feel that Roberto Martinez’s current team are in with a good shout this season.
The likes of Romelu Lukaku, Ross Barkley and Gerard Deulofeu are in fine form following a slow start to the campaign.
And Cleverley, who made his first start since August in midweek after returning from an ankle ligament injury, insists the Toffees are determined to get their hands on silverware in 2016.
The 26-year-old former Manchester United midfielder told the Echo: “You have got to be confident going into a semi-final.
“We’re are hungry, young and enthusiast squad who want to win things. We see this as an opportunity and we will be giving it everything.
“Let’s hope we make it to the final. You want those trophies and from my experience last year with Aston Villa, I know that momentum in the cups can lift the whole club and help your league form.”