The French central defender expressed his belief that the Toffees have sufficient quality to pull through a hectic run of games despite not possessing a large squad
The Toffees were held to a 1-1 draw by Sunderland in their quarter-final meeting on Saturday at Goodison Park, meaning that they face a trip to the Stadium of Light for the right to take on Liverpool at Wembley in the semi-final.
And Distin believes that David Moyes' squad must quickly adjust to a busy period if they are to present their manager with his first piece of silverware in his 10th year in charge on Merseyside.
"It’s physically tough but that’s why we have all the great physios to help us recover between games," the centre-back told The Liverpool Echo.
"That’s the most important when you’ve got games together like this.
"All together it’s going to be seven games in three weeks, and all you can do is recover and make the most of the three days between games.
"You can’t train much, you have to rest your legs and go for massages and ice baths. But so far, so good.
"We’ve only got a small squad but we’ve got a lot of quality, and it’s up to the manager to make decisions on whether he rests people or not.”
Everton are 11/2 with Bet365 to draw 1-1 for the second game in succession when they take on Arsenal next time out.
Moyes' men face the Gunners on Wednesday before a trip to Swansea City at the weekend.