The Black Cats fell behind when Theo Robinson opened the scoring nine minutes before half-time but Johnson’s side improved after the break.
Nathan Broadhead drew the Wearsiders level in the 52nd minute and both sides had chances to win the match in 90 minutes.
The draw meant Sunderland earned the point they needed to top the group following wins over Lincoln and Manchester United Under-21s.
It means the Black Cats will play at home in the first knockout game of the competition in the next few weeks.
Despite already being through, Johnson named a strong side against Bradford to try and win the match.
Our chief SAFC writer Phil Smith has delivered his verdict on how each player fared at the Stadium of Light:
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1. Thorben Hoffmann - 6
Little he could do about the goal. One or two uncertain moments on the ball very early on but for the most part assured in possession and gathered crosses well enough. Made one fine late save and one good penalty stop. 6 Photo: JPI Media
2. Kenton Richardson - 5
Missed a good chance just before half time at the back post. Didn’t get forward a great deal otherwise but defended OK. 5 Photo: JPI Media
4. Oliver Younger - 6
Steady enough in defence and generally looked after the ball well. 6 Photo: JPI Media