The Potters appeared set for a comfortable night when they led 3-1 against a side down to 10 men with just five minutes left to play but Birmingham scored twice late on to force extra-time.
Kenwyne Jones struck for Stoke when the extra-period began but the hosts levelled once again in the 118th minute and the Premier League side only advanced after a 4-2 success in a subsequent penalty shoot-out.
And Shawcross said: "It's brilliant we're in the next round but that's the only thing we take from the game to be honest.
"It was a very disappointing performance from everyone and we need to have a good look at ourselves before Saturday to make sure we're better because that's not good enough.
"To get through to the next round is great but you've got to have the performance to match that. We should have cruised through the game but we didn't.
"We've got to be more professional, we've got to see the game out. It's a disappointing performance but ultimately we're through to the next round."