There were 12 yellow cards during the match, which featured two mass brawls.
Both sides may face retrospective action from the Football Association, with Spurs' Mousa Dembele having appeared to gouge Diego Costa's eye.
"It is not nice to see for kids here or kids watching on TV, I apologise if it looked bad on TV," said Rose.
"It is a London derby. It is to be expected. 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."
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It was an emotional London derby at Stamford Bridge on Monday night, with Tottenham being shown nine yellow cards, the most to a single team in a match in Premier League history.
Spurs needed to beat Chelsea to retain hopes of winning the Premier League but squandered a two-goal lead, which saw Leicester crowned champions for the first time in their history.
Spurs boss Mauricio Pochettino stepped onto the pitch at one point to separate Rose and Chelsea's Willian in the first half, and at full-time the 25-year-old full-back was involved in an incident that resulted in Blues boss Guus Hiddink being pushed to the floor.
"I couldn't tell you what happened, it was just handbags being thrown," said Rose.
"I saw the Chelsea manager fell on the floor. I hope he is all right. 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."
Hiddink said: "It was a very emotional and hectic game. To be honest, there were some incidents which were not good. There was a bit of verbal animosity and I tried to come in-between and go into the locker room.
"Everyone started dancing around and pushing around. More people became involved and we shuffled around. You must not have these type of incidents but it happens and at the end we must all calm down."
The Dutchman also played down the incident that saw him pushed to the floor, adding: "If you have done some judo and wrestling you can easily fall. Even at my age, I had no problem to fall down."
Tottenham defender Danny Rose has apologised for the ugly scenes that marred Monday's 2-2 draw with Chelsea at Stamford Bridge.