Despite playing a weakened team the Latics had the better of the chances but couldn't break the deadlock against a determined City outfit who won the game on penalties.
Speaking about the loss, Martinez said: “It was a disappointing night because it’s a competition we wanted to go far in and were looked forward to the first home cup tie in a long time.
“I felt we did everything we had to in terms of the performance needed, showing patience against a unified and organised Bradford City side and creating numerous chances.
“We had a goal disallowed early on but continued to get into good situations that we just failed to capitalise upon, but we never lost that composure in our display and kept a clean sheet for the 120 minutes.
“Ultimately when you create that amount of chances and don’t hit the back of the net it becomes very difficult to win a football match.
“Then, when you go into a penalty shoot-out the luck is out of your hands and it wasn’t going to be our night.
“The shoot-out is the perfect assessment of the evening; the two most assured takers were the ones who missed their chances and that was typical of the night.
“But we congratulate Bradford City and wish them well in the next round whilst looking internally at how we can continue to improve.”
Bradford now progress into the quarter finals of a cup competition that Latics fans were hopeful of seeing their side reach Wembley.