On-field referee Anthony Taylor missed the incident, and Spurs seconds later scored a last-gasp equaliser through Harry Kane, and Dean has admitted he did not alert his colleague to the incident because he wanted to spare him "more grief".
"I missed the stupid hair pull at Chelsea versus Tottenham which was pathetic from my point of view," Dean told the Up Front podcast. "It's one of them were if I had my time again, what would I do? I'd send Anthony to the screen.
"I said to Anthony afterward: 'I just didn't want to send you to the screen after what has gone on in the game'.
"I didn't want to send him up because he is a mate as well as a referee and I think I didn't want to send him up because I didn't want any more grief than he already had."
Dean, who refereed more than 550 matches in the top flight and became a full-time VAR official last season, was taken off VAR duty for two months after the controversial match.
In July the Professional Game Match Officials Limited (PGMOL) said Dean was stepping down from the role and leaving the referees' body.
"That was a major error. If they don't score from the corner it is not as big an issue," said Dean, who had acknowledged his mistake at the time of the incident and says VAR duty used to leave him "dreading" matchdays.
"I knew full well I would be stood down the week after. I asked to take a bit of time off because it wasn't for me.
"I used to get in the car on a Friday and was dreading Saturday. I was thinking, 'I hope nothing happens' ... I used to be petrified sitting in the chair."
Additional reporting by Reuters.