First-half goals from Danny Higginbotham and Mamady Sidibe put the Potters in control and Matthew Etherington added a third after Chris Samba had seen red for a second bookable offence.
"It was poor defending on two separate occasions in the first half," Allardyce said.
"It's taken the game into Stoke's hands and it's pretty poor defending from our point of view to say the least. "It's one that we've worked at over the last few days and unfortunately the lads haven't taken that onto the field.
"In a very competitive game like this you have got to do your job right in those areas and had we taken the opportunity to defend right, certainly on the second one, and just come in (at half-time) 1-0 down, we would have looked to have gone on from there."
Source: PA
Source: PA