City looked to be on their way to claiming maximum points when Nicky Maynard's 11th goal of the season gave them a 1-0 lead just short of the hour mark.
However, the visitors grabbed an equaliser Youl Mawene just 12 minutes later.
"We were a goal away from a good performance but a couple of mistakes cost us dear and now our play-off chances look slim," Johnson said after the match at Ashton Gate.
"While it's still mathematically possible for us to finish in the top six we will be giving it all we've got. But we can't afford any more basic errors.
"We played the sort of football I want and I felt we should have been ahead at half-time.
"There were chances in the second period, but the ball didn't quite break for us where it matters most."