City led 2-0 at half-time but lost 3-2 after Kieran Lee's 96th-minute winner.
Both teams had a player sent off, with Gary O'Neil dismissed seconds after Lee Tomlin's penalty bounced clear off the post when Johnson's side were 2-1 up.
"There was a turning point in the game. You couldn't make it up, it's like a bad dream," he told BBC Radio Bristol.
"What we have showed is that we can go to a real intense environment and really silence everyone, especially for 45 minutes.
"Whether you win or lose, you always learn from it. It's taught me, I know who can't quite handle the pressure and that's interesting."
City have 10 points after their first seven Championship games of 2016-17, having won their first two matches.
Bristol City head coach Lee Johnson says their loss at Sheffield Wednesday showed him which of his players "can't quite handle the pressure."