The host led 2-1 going into the dying seconds at Stamford Bridge, before Spurs were awarded a late corner with Argentina international Romero appearing to pull Chelsea defender Marc Cucurella to the ground by his hair during the build-up.
There was a pause in play while Dean took time to review the incident at Stockley Park, but he decided against sending Taylor to the pitchside monitor to consider a red card and play was restarted.
Harry Kane then headed in a dramatic late equaliser before head coaches Thomas Tuchel and Antonio Conte clashed at full-time, with both receiving red cards after the final whistle.
While Dean acknowledged that he could not have given Chelsea a free-kick through VAR, he accepted that he should have sent Taylor to look at the incident.
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."
Prior to the injury-time incident, there were also complaints from Chelsea over Spurs' first equaliser in the 68th minute.
A sliding challenge from Rodrigo Bentancur on Kai Havertz was deemed not to be a foul, before there were claims the flag should have gone up with Richarlison stood in an offside position and obstructing goalkeeper Edouard Mendy's view as Pierre-Emile Hojbjerg stroked the ball home.
But Dean believes he was right to let Hojbjerg's goal stand, saying: "This one was relatively straightforward. I can't go back 44 seconds to look at Rodrigo Bentancur's potential foul on Kai Havertz.
"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."