Dean was on VAR duties when the game at Stamford Bridge ended in a 2-2 draw.
Chelsea held a 2-1 lead until second half stoppage time when Romero pulled Cucurella down by his hair but referee Taylor and his VAR team took no action and the visitors scored from the ensuing corner to nick a point.
The incident was another sideshow in a game that saw opposing managers Thomas Tuchel and Antonio Conte sent off after the final whistle over a post-match handshake gone wrong.
In his column with the Daily Mail, Dean said: "Sometimes in hindsight, you realise you could have acted differently. I've now had time to reflect on Sunday's clash at Stamford Bridge.
"I asked referee Anthony Taylor to wait while I looked at the incident involving Tottenham's Cristian Romero and Chelsea's Marc Cucurella. I could not award a free-kick as VAR, but I could recommend to Taylor that he visit the referee review area to consider a possible red card.
"In the few seconds I had to study Romero pulling Cucurella's hair, I didn't deem it a violent act. I've since studied the footage, spoken to other referees and, upon reflection, I should have asked Taylor to visit his pitchside monitor to take a look for himself.
"It goes to show that no matter how experienced you are - and I've spent more than two decades as a Premier League official - you are always learning."
Dean however acknowledged that he was right to allow Tottenham's first goal to stand after Chelsea complained of a foul on Kai Havertz in the build up and Richarlison blocking the view of Edouard Mendy from Pierre-Emile Hojbjerg's shot.
"This one was relatively straightforward. I can't go back 44 seconds to look at Rodrigo Bentancur's potential foul on Kai Havertz," Dean added.
"The question was whether Richarlison was interfering from an offside position. When Hojbjerg's shot was struck, Chelsea goalkeeper Edouard Mendy had a view of the ball for me. His line of vision wasn't clearly blocked, so it was onside and 1-1."
