The hosts fell behind to Gary Taylor-Fletcher's brilliant effort before goalkeeper Adriano Basso was sent off for handling outside his area.
However Johnson junior, who has been criticised by supporters in recent weeks, struck with two minutes left to salvage a point and continue City's promotion push.
The result leaves the Robins five points behind leaders Oldham and Johnson insisted that some of his players were not good enough.
"I know my players and Lee is capable of creating or snatching a goal when we need it," said Johnson. "He is strong enough to cope with any negative comments.
"It was a poor performance by us. We never got going and a number of individual players had to be told that their contributions weren't good enough," Johnson added.
Huddersfield boss Peter Jackson believes his side can take a lot of encouragement from their performance.
The result means Huddersfield are now seven points away from the League One play-off positions and Jackson hailed goalscorer Taylor-Fletcher.
"It was a great goal and we had enough chances to win by five or six goals," said Jackson.
"It feels like a defeat and it says how far we have come that we are upset at getting a draw at a club with such a good home record as Bristol City.
"There were so many positives for us and we can take a lot of encouragement for the rest of the season from our performance," Jackson added.
Sporting Life