It was quick thinking from Kyle Walker, whose quick free-kick found Emmanuel Adebayor who shot it past Tim Howard to give Spurs the vital win.
"Everton were very unlucky and will be very disappointed with the result," said Carragher on Sky Sports.
"It was quick thinking from Kyle Walker - that free kick was five yards out in the wrong position, you could say they got an unfair advantage because they went on to score but when you take a free-kick back you get away with it.
"If you took the free kick five yards forward, then I think you would be in trouble. But Jagielka and Distin are just not watching the ball - they are experienced defenders and you are told as a kid never to switch off.
"Credit to Walker for seeing it and Adebayor - well, that was Drogba-like and you want to see more of that type of thing from him; using his strength and power."
Carragher also believes that Everton should have got a penalty after Etienne Capoue caught Seamus Coleman in stoppage time, but referee Mark Clattenburg was unmoved.
"That was a penalty, Capoue stuck his leg out, Coleman's got there first and is brought down. It is a blatant penalty.
"Everton were very unlucky - never mind the penalty claim but they were dominant throughout; Spurs should get a massive lift from this game -they have not played well but have beaten one of their rivals."