The Potters looked poised to routinely book their place in the last eight of the competition as they led 3-1 against 10-man Birmingham with five minutes remaining, only for Peter Lovenkrands to score twice late on amid a pulsating finale to send the game to extra-time.
The Barclays Premier League visitors again stamped their authority on the fourth-round tie immediately after the restart courtesy of Kenwyne Jones, yet Blues once more levelled in the 118th minute through Olly Lee to make it 4-4 and round off a dramatic clash.
Stoke, however, eventually progressed 4-2 in the subsequent penalty shoot-out to book their place in Wednesday night's draw.
"It's brilliant we're in the next round but that's the only thing we take from the game to be honest," centre-back Shawcross told Stoke City Player.
"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 and 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. The gaffer has just said that, he's not happy with us. It's a disappointing performance but ultimately we're through to the next round."
Stoke boss Mark Hughes wants lessons to be learned as the Staffordshire club now look to reverse a disappointing run in the league which has seen them fail to register a victory since the end of August.
"We need to look at it again and learn from it," Hughes said.
"We did a lot of good things, in fairness, to put ourselves in a decent position but obviously the last 45 minutes or even hour of the game in terms of the extra-time, that wasn't what was required and wasn't really acceptable from our point of view.
"It's just that last period that's really disappointed us. We need to learn from that, and we will do. I think it's important that we understand that in similar circumstances, what happened can't happen again.
"We've got to be a lot more professional in terms of our understanding of what is required and use a little bit more football intelligence."
Birmingham's brave fightback having played for close to an hour-and-a-half with 10 men ensured there were plenty of positives for the hosts to take into their Sky Bet Championship campaign.
And midfielder Lee, who levelled matters towards the end of extra-time to force penalties, hailed Blues' never-say-die attitude.
"It was a crazy night," Lee, son of former Newcastle and England midfielder Rob, told the club's official website.
"We're unfortunate to come out on the wrong side but the boys gave everything, they gave 110 per cent and obviously it's a lottery when it goes to penalties so we were just unlucky this time.
"We've got a great bunch of lads here and we're all together as a group, we just tried our very best, even at 3-1 down we thought we can get back into this and kept plugging away, luckily the ball fell for us and we had Peter Lovenkrands to put the ball in the net."
Lee added: "Just before the penalties were taken, me and Dan Burn were speaking and we said 'today's our day' but it was not be. Although it was a great effort from the lads and you can't ask for much more."