The Bantams, who are still in the FA Cup and host Arsenal in the quarter-finals of the Capital One Cup next week, advanced to the last four of the Northern Section with goals from Ritchie Jones and Craig Forsyth early in the second half at Vale Park.
Adams said: "We were poor individually and collectively and we've gone out of the competition in a fashion that doesn't please me.
"I did think Jennison (Myrie-Williams) was tripped and we should have had a penalty, and there was also a handball right in front of me before the first goal. Having said that, I'm not looking for excuses.
"I don't want to take anything away from Bradford because I thought they were excellent.
"They were better than us and the players they brought in showed more desire than the ones we brought in, so that's obviously very disappointing.
"This game has given me more questions than answers and I'm just thankful it wasn't a league game.
"We are enjoying a good season in the league and I think you will see a better performance when Chesterfield come here on Saturday."