Monday's stalemate also saw Spurs midfielder Mousa Dembele appear to poke Diego Costa in the eye and Tottenham winger Erik Lamela step on the hand of Chelsea's Cesc Fabregas as he was picking himself up following a heavy tackle.
"It is not nice to see for kids here or kids watching on TV, I apologise if it looked bad on TV. It is a London derby. It is to be expected," Rose told British media.
"We wanted to win and they wanted to stop us having any more say in the title race. There are no bad words to say about Chelsea. These are the games you want to be part of. It was a great game."
Spurs will be hit with an automatic sanction from the Football Association (FA) as any team that receives six or more bookings during a game are ordered to pay at least 25,000 pounds in fines.
Outgoing Chelsea manager Guus Hiddink, who tried to calm the situation on the touchline, was also knocked over during the brawl.
"I couldn't tell you what happened, it was just handbags being thrown. I saw the Chelsea manager fall on the floor. I hope he is all right," Rose said.
"People were saying from the bench that he conducted himself like a true gentleman throughout the whole game. He did not want any trouble to be started."
The London clubs are expected to be charged with failing to control their players, with Fabregas accused by the British media of sparking the scuffle by flicking at the groin area of Tottenham's players and coaching staff.
Chelsea defender Gary Cahill hope the FA would show leniency by taking into account the significance of the game.
"Sure it boiled over at times, but that's because there was so much at stake," Cahill said.
Chelsea, who are ninth in the table, travel to relegation-threatened Sunderland on Saturday, while Mauricio Pochettino's charges host Southampton the following day.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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