With McCall's men temporarily down to ten men as Rory McArdle left the pitch for five stitches in a head wound, City conceded twice in quick succession through a Chris Maguire penalty and a stunning drive from distance by Marvin Johnson to put the hosts in control.
Johnson's screamer past City shot-stopper Rouven Sattelmaier came exactly five minutes after McArdle had left the pitch to go down the tunnel at the Kassam Stadium for treatment.
In the end, McArdle was replaced as a precaution by Daniel Devine, although the centre half was reported to be fine after the match.
Jordy Hiwula netted his tenth goal of the season late on but City, who arguably enjoyed the better of the play up to Maguire's opener, were unable to continue the fight-back and take the rearranged last-eight tie to penalties.
McCall said: "I feel for the supporters and the players after this one because we were the better side for long periods, especially in the first half, and it was just a five-minute period or so after the break that has cost us.
"We had to wait a long time for Rory to get his stitches done. During that time, we find ourselves two goals down.
"There were no arguments about the penalty for the first goal, and their second goal is just a world class strike. Even with twelve players on the pitch we wouldn't have stopped that.
"That period when we were down to ten men was certainly the turning point in the game though.
"We have definitely been unfortunate in that sense.
"For the lads to then be two goals down and see their dreams of getting to a Wembley final in this competition slipping away, it was all credit to them to try and fight back in the game.
"I felt we deserved to take the game to penalties at least tonight (Tuesday).
"We know we have a good group in the dressing room, however, and we look forward to Saturday now, with new players, a new shirt (#BantamsFamily fourth shirt), and hopefully a big crowd at home to Gillingham."
One new player likely to be on show against Gillingham in the #BantamsFamily fixture at the Northern Commercials Stadium is Charlie Wyke after the striker's deal from Carlisle United was confirmed this Tuesday evening.
City also revealed deals for defenders Kevin Toner, Jacob Hanson and Matthew Penney (pictured below) on a busy transfer deadline day for the Bantams.
McCall added: "I'm obviously delighted that we've managed to get the deal over the line for Charlie.
"Greg (Abbott), James (Mason) and Edin (Rahic) have worked tirelessly back at the stadium to sort everything out.
"He's certainly shown in the last two seasons that he knows where the back of the net is, and he will give us greater physicality up front after losing James (Hanson).
"We were close to other signings but they didn't quite come off through no fault of our own, so we go into this final period of the season with five strikers if you include Marshy (Mark Marshall).
"With Billy (Clarke), Jordy (Hiwula) and (Alex) Jonesy, I believe that is enough firepower, especially if we play with the same desire and application as we did tonight (Tuesday).
"Losing Killa (Matthew Kilgallon) to injury was clearly a massive blow to us.
"With the window closing, you need those options in your squad and those extra bodies in. We've managed to achieve that with the three young lads we have brought in."