Chris Taylor was disappointed to have "dropped two points" following a 1-1 draw at Macclesfield Town.
The Bantams had the opportunity to move within three points of the Sky Bet League Two summit, though proved unable to overcome their Cheshire hosts.
Taylor believed City missed opportunities to give themselves a stronger foothold in the game and must show a response, going forward.
The midfielder said: "We dropped two points at Macclesfield, I would definitely say.
"In the first half, we were in control and had chances to go 1-0 or even 2-0 up, then gave away a penalty we did not really need to.
"In any game, if you do not take your chances, there is always a chance - even when you are on top - you can be caught out.
"We gave ourselves everything to do and it was always going to be tough to break them down because they are a very well-organised team.
"It was a frustrating afternoon but we had to take a point and make sure we do better to try and get three points, next week."
Despite his deflation, Taylor was proud to have made his full debut in claret and amber, at Moss Rose.
The former Blackpool man alluded to a feeling of relief and is looking forward to gathering more minutes over the coming weeks and months.
"It was huge for me to make my first league appearance and my full debut for the club. I felt good," the 32-year-old added.
"It was my first 90 minutes for City and my first 90 minutes in a while, so I was really happy.
"There are obviously areas to improve on, as with everyone, but I have not had the game time some of the other lads have had.
"I feel fit and ready and, if I did not, Gary (Bowyer), probably would not have picked me.
"Hopefully, I repaid him a little bit and can continue to kick on, now."
Bowyer’s side return home - next Saturday - in Sky Bet League two action against Newport County. CLICK HERE to purchase tickets.