City crashed 3-0 against Tranmere Rovers at Valley Parade to miss out on a potentially lucrative third-round fixture.
Bradford play host to Leyton Orient today seeking to exorcise the demons of that result and to book their place in the third-roun
d draw.
And McCall is adamant his side must do themselves justice this time.
"I've told the players that we don't want to be going out of the Cup with a whimper," said McCall. "No one wants that.
"Last year, we never turned up and we never gave the crowd the chance to get behind us or get excited.
"Tranmere were really solid and played well, but we were poor and did not look like getting anything.
"We don't want that to happen tomorrow. You can't ever guarantee a result but I would like to think we'll go out and give it everything and put in a really good performance.
"Hopefully, that will be enough to see us through but the main thing is that we give it a proper go and do ourselves justice."
Bradford must break down an Orient defence which has not conceded a goal during the last five games.
But McCall believes his team possess the necessary firepower.
"Orient are on a good run and will be very tough to break down – the stats don't lie and to go so long without conceding a goal is a great achievement.
"But this is a big opportunity for us; everyone dreams of getting through to the third round and every extra penny can only help the club."
Bradford have announced a special season ticket offer to help their fans through the credit crunch.
The club are offering cut-price season tickets for the 2009-10 campaign during a special offer running throughout next month.
Bradford chairman Mark Lawn explained: "We just wanted to do something for our fans to help them through this difficult period.
"The credit crunch is starting to hit hard and we wanted to do this for our loyal supporters.
"Under the offer, season tickets will be available for £99 in the TL Dallas Stand and £138 for the rest of the ground.
"It means an adult can come and watch Bradford City next season for just £4.30 a game."
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