Despite a spirited performance from the Bantams' Under-18s at Turf Moor, goals from Burnley duo Dwight McNeil and Tommy Wood secured the Clarets a home encounter with Norwich City in the next round.
McNeil gave the hosts the lead on the stroke of half time before he turned provider to set up Wood for Burnley's second ten minutes after the restart.
City, who were already without regular skipper Niah Payne going into the game due to injury, were forced into a reshuffle early on when right back Tom Windle went off with a foot problem.
Thornber said: "I felt we had quite a bit of possession but we perhaps lacked that killer edge in the final third.
"I don't think there was too much between the two sides on the night. Just a couple of moments in the game that we got punished for.
"We tried to play football in the right way but we don't have the options to play to a big man up front and mix things up a bit.
"Tom Windle going off so early on was a bit of a blow for us.
"We had to change things around - putting Kwame (Boateng) at right back - but it at least gave us another chance to have a look at one of the Under-16s (Jake Maltby).
"Jake didn't look out of place when he came on. He kept the ball moving in midfield.
"We were gutted that Niah Payne, our captain, couldn't play but it opened up the door for young Christian (Farrar, another member of the Under-16 squad).
"He has a lot of pace and did himself credit during his time on the pitch.
"Even going into the break having just conceded, we were quite positive because we felt we could get back into the game.
"Being two-nil down in the second period, we decided to go to three at the back and three up front.
"We had a couple of balls flash across the box late on. If one of them goes in, you just never know.
"Even though the result isn't what we wanted, we can't be too disappointed about our performance. There was a lot of positives to take out of the game.
"This level of football is all about player development, and I thought the lads acquitted themselves well.
"Coming to a Premier League venue like this (Turf Moor) is also a great experience for our group."
Bantams Player HD subscribers can watch Steve Thornber's full post-match interview by clicking HERE.
Fans can see a snippet of the interview by clicking on the video screen below.