Goals from Sergio Aguero and a brace from Alvaro Negredo gave City a 9-0 aggregate success over the Hammers to send them to Wembley.
And while West Ham put in an improved performance in comparison to the first leg drubbing, Allardyce admits that their defending was still poor as they went behind just three minutes into the return leg at Upton Park.
"The most disappointing thing was the defensive unit doing what it did in the first few minutes," Allardyce told Sky Sports.
"Man City are a super, super team - but that was not a super, super goal - that was bog standard defending not done correctly and that was really disappointing.
"I thought we may have come back through Kevin Nolan's goal straightaway but as our season is going that was offside.
"You can't do mistakes at this level to the level we did, far too many errors in our half - there was a fair bit of action in Man City's box, but no clear cut chances for the amount of time we had in their final third."
Allardyce is hoping a bad night was not made worse by injuries to Mo Diame (knee) - who was stretchered off - and Joe Cole.
"Joe's shouldn't be too long. Mo's looked more serious - and until a scan we don't know - but (the medical department) are saying it may not be as serious as first thought," he said.
"Still I think he would be out for a little while."