Midfielder Darron Gibson and striker Arouna Kone are out with long-term knee injuries while left-back Leighton Baines has been sidelined with a broken toe and on-loan Barcelona forward Gerard Deulofeu has now been ruled out for several weeks with a hamstring strain.
James McCarthy served a one-match ban last weekend but in his absence Leon Osman replaced him and scored the opening goal of a 4-1 win at home to Fulham while Kevin Mirallas came off the bench to also score.
However, midfielders Gareth Barry and Ross Barkley and goalkeeper Tim Howard are just one yellow card away from suspension and that is something the squad must cope with according to Martinez.
"It's that time of the season," said the Toffees boss, whose side sit just one point outside the top four having been beaten just once in the league all season.
"We have Kevin Mirallas on three bookings and the three players mentioned (on four).
"Having the amount of minutes (they have on the pitch) you are going to get these threats and that is not going to change anything.
"All we are doing is taking it game by game and making sure everybody is fully fit for the games they are involved in and nothing else."
McCarthy returns for Sunday's trip to Martinez's former club Swansea having made an instant impact since his £13milion move from Wigan along with the manager in the summer.
Martinez believes the 23-year-old, who has already played more than 250 matches at club level, is an outstanding example to modern players.
"When you're talking about players who you want to set an example to the youngsters, he's clearly that," he told evertontv.
"To be able to reach that landmark at that age shows you that he's never changed, he just embraces challenges.
"He wants to get in positions where he can help the team and he's such a humble footballer and example of how a modern footballer should behave.
"Looking at the way he's been enjoying his football at Everton it's been a real joy for everyone and he deserves to be an example."
Everton's hopes of getting Deulofeu back before the end of January appear to have been dashed with his parent club giving a more pessimistic prognosis.
On Tuesday Martinez said he thought the 19-year-old would be missing "for the best part of five weeks".
However, Barcelona have increased that timescale to up to two months.
"The striker Gerard Deulofeu, who played this season on loan to Everton, will recover from injury in Barcelona in co-ordination with the medical services of the English club," said a statement from the Catalans.
"The player has this afternoon undergone testing by the medical services of FC Barcelona have confirmed the biceps femoris muscle injury in his right leg.
"The downtime is approximately six to eight weeks. The recovery will be in Barcelona in conjunction with the medical services of Everton FC."