Latics went into the last-16 tie having beaten Nottingham Forest 4-1 away in the second round and then West Ham by the same scoreline at Upton Park in round three.
Many would have backed Wigan to get at least another four goals at home last night against npower League Two Bradford, the lowest-ranked team left in the competition, and Wigan created a host of opportunities.
They were unable to convert any of them over 90 minutes or during extra-time, though, and having held on for the 0-0 draw, a spirited Bantams side then went on to win the subsequent penalty shoot-out 4-2 and book a place in the quarter-finals.
Latics midfielders Shaun Maloney and Jordi Gomez failed to put away their spot-kicks, and Martinez said: "We are disappointed because we were really looking forward to the fourth round of the Capital One Cup.
"We have had two very good performances away from home where we have been clinical and scoring many goals.
"The last thing I expected was that if we created chances we would miss them. That leaves a feeling of frustration and disappointment."
Martinez made nine changes to his first XI from Saturday's Premier League win over West Ham, handing first club starts to midfielders Fraser Fyvie, 19, and Danny Redmond, 21.
Another 21-year-old, forward Callum McManaman, was also included and Martinez thought the trio fared relatively well, although he did sense that as time went on without Wigan scoring, some of the players who had come into the team were beginning to feel the pressure of expectation.
"I thought the younger players had a massive role in the game and in many ways, we did everything we had to," Martinez said.
"Bradford had to defend really well. I thought they worked extremely hard and were disciplined and well-organised.
"But you have to score early.
"I think we had two or three good opportunities early on, and possibly with the one where Mauro (Boselli) gets in front of the goalkeeper, if we had scored that goal it could have been a very comfortable win.
"But we missed that chance, and it became a bit of a feeling that the players really wanted to do well because it was their time to impress and be important on the pitch.
"It then became a harder job."
Bradford manager Phil Parkinson paid tribute to the club's supporters for the way they had helped drive the team on.
"I have to say that the support we had was great," Parkinson said.
"When you have tired legs out there, it kind of gives you that extra impetus to keep going and you could sense that with the players - a few of them were cramping up, but the supporters just urged the lads on and got that extra bit out of them.
"It is so important, and I said to the lads afterwards that the supporters we had there are the reason we are all at Bradford City."