The Toffees' chances of playing in the Europa League were virtually ended when they lost at Manchester United and city rivals Liverpool beat Birmingham to move five points clear in sixth place with four matches remaining.
But even if they can claw back lost ground, the long-serving Hibbert, an Everton academy graduate, is already thinking about next season and ending the club's 16-year wait for silverware.
"Whatever cup it is, we need one next season," said the 30-year-old. "Everton need silverware - the sooner the better.
"Europe is a great achievement for any club, and it's a great experience for the fans to get away to talk about and sing about.
"I think the squad is big enough for Europe. We've got some good players in depth. We've got a lot of injuries again which doesn't help but there is quality there. I think the squad we've got is capable of challenging in the domestic cups and Europe."
Source: PA
Source: PA