City could have gone fourth in the table with a win at St Andrew's but remained in eighth place.
Johnson, who did not attend the post-match press conference on Wednesday night, said: "Getting beaten 1-0 at Birmingham is no disaster, but we didn't give it enough of a go. Not enough players produced their best football and that's what I was angry with because the prize was so big.
"I'm always disappointed with a defeat but I get angry with the manner of a defeat sometimes. On the day only a few individuals performed and we certainly didn't do enough to win the game, and that's why I was so disappointed.
"The prize was a fourth-place spot and I didn't feel enough of them showed me in their body language that they wanted to get it."