Birmingham tasted defeat at home for the first time in 13 months and manager Alex McLeish was unhappy with the boos which greeted his team at the final whistle.
An own goal from Roger Johnson and a goal from Tim Cahill gave Everton their first win of the season.
McLeish said: "I don't think any of us deserved the reception (at the end). I don't think it was fair the fans should boo us for losing the game or indeed the performance because it wasn't a bad performance.
"The players deserve a lot of credit for what they've done over the past year. It is the culture we live in. Players are paid big wages and the fans are expecting them to deliver.
"You can't blame them for that. We do live in a society where every little move is scrutinised. There is no doubt there is more fickleness than ever before.
"We have to take it on the chin. I don't think we should have been booed and that's all I'm saying on it."