Since his arrival in the summer of 2009 Martinez has progressed past the fourth round of any knockout competition just once, with the Latics going on to lose to Arsenal in the quarter-finals of the 2010-11 Carling Cup.
Wigan's six other cup appearances under the Spaniard have seen them fail to get past the fourth round and, in the FA Cup, two of the previous three seasons have seen them exit to npower League One sides Notts County and Swindon, who were in League Two at the time.
The fact Martinez makes significant changes for cup competitions and plays youngsters - with Tuesday's third-round replay against Bournemouth unlikely to be any different - goes some way to explaining their results.
"In my eyes they are strong players or they wouldn't be with us," he said.
"It is all good for me to say I want to look at the youth, give opportunities to the young players and create a path to the develop the youngsters if I am not going to be brave enough to give them opportunities.
"I want to create something special at the football club where we can develop our youngsters.
"In the last game against Bournemouth we saw the debut of Roman Golobart, who has been on a three-year programme.
"He was sent on loan to Inverness in the Scottish Premier League and he has come back stronger - there are some youngsters that deserve that opportunity.
"If we don't win, I will take that responsibility but I will never be shy of giving youngsters opportunities and making sure that we are producing our own players.
"I think it is important you share the demands and progressing in the cup is as important as winning football games.
"Sometimes it can be unfair to put a youngster out in the Premier League when they are not ready because the gap between Under-21 football and the first team is huge.
"Sometime having a competition in between, which is vital to win because we want to win in every competition, is something that as a club and a manager we need to be brave enough to give youngsters opportunities."
A draw at Fulham on Saturday kept Wigan out of the top flight's bottom three on goal difference.
Striker Franco di Santo scored an impressive equaliser for his fourth league goal of the season and first since October, but with Arouna Kone at the African Nations Cup he is unlikely to feature tomorrow.
The Argentinian's contract expires at the end of the season and he has already been linked with other clubs, with Martinez keen to hang on to the 23-year-old.
But any deal to extend Di Santo's stay at the DW Stadium will probably have to wait until May.
"When you get into this moment of the season the priority or essential focus is keeping Wigan in the Premier League," said the Latics boss.
"As you know, we will lose players, we will have to move players on and we want to keep players.
"But all I am focused with on Franco is developing him, helping him keep fulfilling the potential he has got as a footballer and just having the impact he had at Fulham.
"That is my only concern because all individual situations need to behind the big goal of Wigan staying in the Barclays Premier League. That has to be our priority."