Nine-man Spurs suffered their first loss of the season in a chaotic game which saw two red cards, five disallowed goals, and a number of injuries.
After a blistering start, Tottenham's fortunes changed when Romero conceded a penalty and got sent off for a high challenge on Argentina teammate Enzo Fernandez.
It came moments after the centre-back went unpunished for a petulant kick on Chelsea defender Levi Colwill.
Destiny Udogie would collect two senseless yellow cards by the 55th minute, but the Blues did not go in front until the 75th.
A valiant Spurs came close to equalising on multiple occasions before Chelsea exploited their high line twice in injury time, with Nicolas Jackson scoring a hat-trick.
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Romero now averages a red card every 18 games for Tottenham, having been shown his fourth, and his three-match ban will coincide with a serious hamstring injury for defensive partner Micky van de Ven.
Ex-Spurs midfielder O'Hara believes Romero brought an uncontrollable temper to the London derby rather than senior leadership.
"Romero has gone five steps backwards today," the talkSPORT host said. "He went out there with this mentality: 'I'm going to hurt someone'.
"In big games, you've got to be a leader. You've played in a World Cup final. You've won the World Cup.
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"You've got to be the calming influence in those big moments. It's a young side. You've got Yves Bissouma, Pape Sarr, Brennan Johnson, Destiny Udogie, Micky van de Ven...
"You've got to be a leader. All he's done is let those players down and he should be ashamed of that.
"He's one of the oldest, where is the leadership?"
Manager Ange Postecoglou refused to criticise Romero after the game and insisted the Argentine's physical approach is an asset.
When asked if he was disappointed with Romero, Postecoglou told talkSPORT: "No, not really. It's part of football.
"Romero has been outstanding for us. He's a very physical defender and that's part of his strength.
"He went a bit too far today, according to the referee, and we have to accept that."