Wales forward Gareth Bale also suffered another injury setback, after making the most of a rare start to put Mourinho's team ahead at bet365 Stadium.
Alli was at fault when his flamboyant flick was intercepted in the build-up to Jordan Thompson's equaliser for the Potters.
The England star's latest mistake drew an angry response on the touchline from Mourinho, who rebuked the star before substituting him minutes later.
Ben Davies put Tottenham back in front with his first goal since 2017 before England captain Harry Kane sealed its place in the semi-finals.
It was Alli's public dressing-down that took the spotlight, with the England international's wretched season hitting a new low in his first start since 27 November (AEDT).
Already exiled for long periods this term by Mourinho and linked with a January move to Paris Saint-Germain, Alli is a shadow of the player who shone during England's run to the 2018 FIFA World Cup semi-finals.
Mourinho made it clear the 24-year-old had to take the blame for his latest blunder.
"Yes, for me a player that plays in that position is a player that has to link and create and not to create problems for his own team," Mourinho said.
"In that situation, an objective counter-attack would probably end with a goal, and it ended with a counter-attack behind our defenders.
"We were unbalanced because when you are in possession you have full-backs out wide and another midfielder in a different line and they caught us in a counter-attack and they transformed the result of the game that was totally in our hands, so yes I am upset."
Tottenham is without a win in its past three Premier League games, including successive defeats against Liverpool and Leicester City, which dented its title challenge.
But Mourinho, a four-time League Cup winner with Chelsea and Manchester United, galvanised his players to avoid an upset in the Potteries.
Tottenham's most recent silverware came in the Carabao Cup in 2008 and it remains in the hunt to end that drought after joining Manchester City and Brentford in the last four.
"To win this trophy we need to win two matches. But they are two very difficult matches," Mourinho said.
"The teams that are going to be there are very difficult teams. Man City are very difficult. Brentford, for me, the way they play they are not Championship, they are Premier League.
"But we are in the semi-finals and we will be there to fight."
Eyebrows were raised when Bale did not return for the second half, but Mourinho said he made the change at the request of the on-loan forward.
⚽️ GOAL!! @GarethBale11 with a glancing header, and even @Socceroos defender @harryjsouttar can't do anything about this one!!!@stokecity 0️⃣-1️⃣ @SpursOfficial— beIN SPORTS (@beINSPORTS_AUS) December 23, 2020
Watch LIVE on CONNECT @kayosports, @Foxtel & Fetch!! ▶️ https://t.co/dR3JmGUdy7#CarabaoCup | #STOTOT | #EFL pic.twitter.com/1sFeMIq7yI
"Yeah, it was his decision," Mourinho said. "Something he felt in the last part of the first half and he didn't want to come out for the second half.
"While he was walking to the dressing room he told me immediately that he couldn't come out for the second half.
"Something I think with his calf. I'm not sure as at that time I just want to reorganise the team and make the change."