Martinez has named the same line-up for his first two matches in charge of the Toffees but will make significant changes for the cup match.
He said: "I think the timing of the League Cup is always really, really good because we are on the back of seven weeks of very strong work from everyone and you get players who are a little bit disappointed because they couldn't show what they could do in the opening two games in the league.
"It's important if we want to be successful over the course of a season that we have a strong squad - not just 11 or 12 players, but a squad of players who are ready to come in, show a moment of form and help the team to get results.
"I want players playing that are fully fresh and recovered. We've got those that played at the weekend, we're going to have another tough game (at Cardiff) and then the international break. So it's important we share that demand and give hungry players a chance to play."
Martinez has insisted there has been no fresh approach from Manchester United for Marouane Fellaini and Leighton Baines - and claimed he has not made a bid for Wigan's James McCarthy.
The Latics have already rejected one bid from United for the pair and there have been reports that a new bid has been made.
Asked if there had been a new offer from United, he replied: "No, no other news."
He told Everton's official website: "I know we are going to be talking about the transfer window but that's not what we are focusing on now."
Martinez admitted he is still looking at new signings ahead of Monday's transfer deadline, but was adamant no bid has been made to his old club Wigan for McCarthy.
He said: "There has been no bid made. I think it's quite easy to understand that James is a player I signed at a young age and I've got huge admiration for him, so it doesn't take anyone (much) to create a little bit of a story. But there has been no bid."