Devante Cole extended City's lead early in the second-half after Joe Meredith had put the hosts in front, but an own-goal from the City defender and a composed finish from Billy Sharp saw United come from behind to leave the Coral Windows Stadium with a deserved point.
Reflecting on the stalemate, Adkins remarked: "Bradford were the better team in the first-half, we started brightly and appeared to have weathered the storm that we knew would come at us, only to go and concede on the half hour.
"We were disappointed to concede in the manner we did and at half-time we changed things tactically, only to concede a second to an unfortunate ricochet.
"But in response we showed excellent character, we were positive and showed belief and a lot of credit goes to the players, including those who came off the bench to have an impact.
"We changed the shape, we put Jose on as a holding midfielder and that allowed him to get on the ball and gave Chris Basham and Louis Reed the license to get forward."
The Gaffer added: "We were dynamic going forward and we scored two good goals, we showed a good attitude to the blow of conceding so early in the second-half and we had a genuine desire to win the game.
"But we have got to cut down on the goals we are conceding, we will continue to work hard behind the scenes, to improve the players we have whilst trying to add to the squad if possible.
"We applauded the supporters afterwards and they applauded us, they stuck with us and we remained in the game and earnt a point."