However, the Spaniard will not be fielding a second-string side as Craven Cottage as it is likely midfielder Darron Gibson will make his long-awaited return from injury.
He also insists loan-signing Romelu Lukaku is fully fit after a head injury and is raring to go again after scoring in the 3-2 win at West Ham.
Martinez believes the fact they are facing fellow Premier League opposition will make it slightly easier in terms of preparation but he will be resting some of his more important players regardless despite there being almost a week until their next league match on Monday.
"It is good we have extra time to recover from the league game but it is more from the West Ham game to the cup game that we have to take into consideration how players are," he said.
"I'm quite pleased we have an extra few days to recover for the Newcastle game but clearly this squad for the Carling Cup game will be based on the efforts of the previous two games.
"I think every game that you play in an official manner is an important game but what is important is that we understand we have to share the demands within the squad and I do feel this squad is ready to cope with that.
"It is that competition I am interested in. I expect a real good performance whichever team is on the pitch.
"We are desperate to get through but it will be a great opportunity for certain players to show what they can do - and even more after what has happened in the last two games raise competition within the squad.
"The squad is big enough to be able to give the time to the players who need to recover.
"To be successful in the cup you need to accept the challenge."
Lukaku, on season-long loan from Chelsea, announced himself on his debut with the winner at Upton Park after coming on at half-time as a substitute.
He sustained a head injury in scoring that goal but Martinez stressed there were no continuing problems and the Belgium international was ready to go again.
"Romelu is fine. We were in yesterday (Sunday) and the reaction has been great," he added.
"The medical department are very happy with him so there are no concerns with Romelu.
"We will keep on top of him but there is no reaction. He trained and he is ready to carry on as normal.
"He had that incredible impact on Saturday with the start of a new career at a new club and a new chapter in your football time.
"It is one of those good feelings you want to carry on and we are really pleased to have him in that frame of mind."
Gibson's return will also be a welcome one for Martinez as it increases options in central midfield.
"Darron I consider fully fit," said the Toffees boss.
"He has been working extremely well and has joined the group so that is a great positive for us."
Striker Arouna Kone could also be involved after being left out at West Ham as he was not entirely right after a knee problem.
"He was 95% at the weekend and we didn't want to take the risk. Kone has a 99% chance he will be available," said Martinez.
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