"I don't always worry about what people think," he said. "But on this occasion it was really important to come out and apologise because of kids watching the game.
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"I told him never to do what I did. He's eight and he plays for Chelsea Under-9s but is very different to me, he's really calm.
"It was really difficult for me after the Barcelona game because I made a mistake but was frustrated that people didn't understand why I reacted. I apologised and everything but I also wanted to show I'm not the person people think I am.
"I'm not a bad guy, I just want to win and sometimes I react."
Having moved on from the incident and made his peace with Ovrebo, Drogba's improved attitude towards his opponents referees has seen him make a remarkable start to the season having scored 12 times in 13 games.
And he said his bid to rights the wrongs of past seasons will continue this weekend as Chelsea play host to Manchester United in a match Drogba sees as an opportunity to make up for an under par performance at Old Trafford last season.
Having lost 3-0 against Sir Alex Ferguson's side in January, Drogba said: "It's not about revenge but I want to make up for last season's embarrassment - I didn't play well that game.
"I had a bad game, the whole team had a bad game, but since then things have changed and the team is in different shape."
Having experienced a turbulent time under the leadership of Luiz Felipe Scolari before the Portuguese coach was sacked, Drogba added that having now rediscovered his form at Chelsea he wants to see his career out with the club.
With the hope of playing beyond the three years remaining on his contract, he said: "I'd like to end my career at Chelsea. I played my first Champions League game at 25 so am still very fresh and hungry. Maybe I'll spend some time in France but I see no reason to leave England when I'm finished."