Second-half goals from Fabian Delph and Scott Sinclair secured a semi-final trip to Wembley for the hosts on the back of a 2-1 win over West Brom in the Premier League during midweek.
But the closing stages of the Villa Park contest were marred by a group of Villa fans entering the field of play and a mass pitch invasion followed
Pulis told BBC Sport: "It's disgraceful. We don't want to see those scenes. They've beaten us and for that to happen, that's just mindless idiots.
"If you're Villa, you need to look at the stewards as they came over to our fans and there was nobody there."
Pulis was similarly furious to see Claudio Yacob given an 80th-minute red card when he collected a second booking for a challenge on Leandro Bacuna.
Villa substitute Jack Grealish was also sent off late on for collecting a pair of yellow cards in the space of 15 minutes.
"I don't know why Jack Grealish was sent off, but I cannot understand why Claudio Yacob was sent off," Pulis said.
"That's a block tackle, something you're taught at five years of age. The referee lets it run on for a few seconds and the disappointing thing is it's two yellows and we can't appeal it. That's going to cost us again when he misses the game against Stoke.
"The referee says Yacob's jumped in to that challenge, but there's enough people moaning about refs without me going on too much."
West Brom enjoyed the better of the first half, but Pulis felt they paid the price for some slack play after the interval.
"We switched off from a throw-in deep in their half of the pitch," he added
"There's two or three things that happened in that movement, which haven't happened since I've been here.
"Up to that point, I thought we were well in control of the game. We've had our chances and not taken them."
