Jordan Willis stepped in for Flanagan, with Dan Neil promoted to the bench.
The Sunderland head coach had said that it had been a close call between the pair for selection in the first place, and that with Flanagan in obvious discomfort, there was no need to take any risks.
"He just picked up an injury in the warm up," Johnson said.
"He just felt his calf, it didn't ping or anything like that, it was just tightness.
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"It was a bit of a Catch-22 anyway in terms of who was going to play centre half, because it was a boggy pitch. We know Bailey [Wright] would come back in because he was fresh, and the other centre-half decision was close.
"With the Shrewsbury game on Tuesday we felt we needed a different attribute [here]."
Johnson also confirmed that Carl Winchester's absence from the squad was due to a minor injury picked up in training on Friday.
The January signing is therefore likely to miss the club's next three fixtures, given that he is cup tied in the Papa John's Trophy.
"He just picked up a slight tweak to his groin during finishing training," Johnson said.
"He just felt it and we think he'll be out for around a week to ten days.
"It's the same with Callum McFadzean, they're not long-term ones."
McFadzean's injury saw Southampton loanee Jake Vokins make his full Sunderland debut in what was an open and fiercely contested game.
Sunderland's head coach said he felt the youngster could have been more aggressive in his defending, but that he improved as the game went on.
Vokins was replaced late on by Dion Sanderson, who again impressed in a brief cameo.
"I thought first 15-20 minutes, he [Vokins] was sparring and not fighting," Johnson said.
"He could have got closer [to the oppositon] and then I thought after that he was good.
"He was good on the ball, there were some nice deliveries and he was energetic.
"Towards the end you could see some fatigue, he's on debut, it's a heavy pitch away from home, and I thought Dion came on and did well.
"I think you're going to find this all over the country now, players sort of hanging in [due to the demands of the fixture schedule].
"Sometimes it will create entertainment like it did today, sometimes it will be create scrappy matches.
"I thought the subs came on and did well, gave us some impetus and we were unlucky at the end not to win the game.
"As we've said before, we need to win games in very different ways as we go into the second half of the season."
The draw leaves Sunderland seventh in League One, seven points behind Hull City in second having played a game less than Grant McCann's side.