Better form at Ashton Gate would have seen them repeat last season's top six finish and Johnson admitted to a feeling of deja vu.
"When (the referee) blew for that free kick it was as if he knew, I knew, the crowd knew and the media knew that the game was going to be drawn," said the manager.
"We certainly know where we have come up short this season and what things need to be addressed during the summer. The last part of the season has fizzled out for us, but there are still a lot of clubs in the Championship who would like to change places with us.
"Our fans showed at the end that they have appreciated our efforts, despite missing out on the play-offs and we will do all we can to reward them next season."
Wednesday boss Brian Laws felt his side deserved at least a point and was pleased with the way they bounced back with Johnson's 25th minute.
Laws went to applaud nearly 2000 travelling fans before the game had kicked off, shaking hands with many of them.
"Our supporters were magnificent," he said. "I'm so glad we were able to give them something to cheer and on clear chances we should have won the game.
"We failed to keep the ball when City scored, but I have to credit the players for keeping going because end of season matches can sometimes be like testimonial games.
"There were plenty of sharp tackles in this one and Darren's free kick was placed into the net with perfection."
Laws refused to be drawn on being linked with City striker Dele Adebola, who came off the bench for the home side in the second half.
Adebola has rejected a new one-year contract with city but Laws said: "It's far too early to talk about transfer targets.
"I'm aware that we have been linked with Adebola, but no business is done at this stage of the year so there is nothing I can say."
Johnson's opening goal followed a turgid opening spell of misplaced passes from both sides.
The little midfielder won a tackle in midfield and then raced forwards onto Nicky Maynard's layoff to stroke the ball home from just outside the box.
City skipper Liam Fontaine made goal-saving tackles from Francis Jeffers and Leon Clarke, while goalkeeper Adriano Basso made several fine saves.
But Wednesday also had a hero in their goalkeeper, Lee Grant, who showed great reactions to keep out an injury time header from Izzy Iriekpen.
Potter's equaliser followed a foul by Fontaine on Clarke, which the City defender contested, but there was no doubting the quality of the goal that followed.