Cotterill, whose side sit two points above the Championship relegation zone, said that his team had chances to take the lead in the first period.
"[The difference was] quality, experience and belief," the manager told reporters at a press conference. "We have been in form as well but we are not talking about an average team here today.
"I thought a few of our boys today didn't look like they have the belief to play in that game. If Sam's shot goes in that might have given us a bit more belief coming in [at half time]."
Birmingham face Millwall in their next league game.