Cardiif sailed into a 4-0 half time lead as City's defence evaporated before them and the visitors added two more goals after the break to earn their first win at Ashton Gate for 40 years.
"It's the sort of night when it is best not to say much," Johnson said after the game.
"Whatever reason I try to offer for that performance will be picked apart.
"We have a lot of soul searching to do over the next few days before our next game at Middlesbrough.
"It wasn't that we forgot how to defend, we just couldn't defend on the night."