The Blues beat Norwich in midweek to reach the quarter-finals, and the Argentine believes they can go much further.
The Blues have made hard work of their progress so far, requiring a penalty shootout to see off Norwich City this week, and extra-time to fight back against Barnsley last time out.
Funes Mori enjoyed a fine evening in the victory over the Canaries, being named as the Blues' man of the match. They now take on Middlesbrough in the quarter-finals, and the Argentine believes they can progress further than that.
“It was a good night for everyone [against Norwich],” he told evertonfc.com.
“It was a tough game. Norwich were very effective with their passing but luckily we were able to win on penalty kicks. We can go on and win this competition. We hope to continue doing our best and keep on reaching the next round.”
Given how long it has been since Everton last won a trophy, this season the Capital One Cup should be a top priority for Roberto Martinez’s side.
Of the big sides, there is only Manchester City left in the competition that teams would like to avoid, meaning the competition is wide open for a number of teams to take seriously.
If they are serious about it, though, the Spaniard will want to start naming full strength sides, with Middlesbrough likely to prove a tough test given how well they are doing under Aitor Karanka in the Championship.