Drogba, who had been substituted after 72 minutes, had to be restrained as Norwegian Ovrebo went down the tunnel.
Blues captain John Terry, who also strongly remonstrated with Ovrebo, defended the reactions of the Chelsea players and Drogba in particular.
"I am fully behind Didier for the way he reacted," declared Terry. "The man wants to win. You can see the passion that he played with during the game and the passion afterwards.
"People are saying we shouldn't have reacted the way we did but the fact is, six decisions went against us in front of 40,000 people. And for the ref to not give one of them is unusual."
The central defender also condemned the decision to select Ovrebo for such a high-profile tie.
"We get a referee who has officiated in 10 Champions League games in his career. For me, for him to be given a semi-final at Stamford Bridge, that's not good enough," Terry told BBC Radio 5 Live.
In fact, the match official has been in charge of 28 Champions League games since 1999, but midfielder Frank Lampard was equally damning of the decisions to reject Chelsea's penalty appeals.
"The penalties are clear as day," he added. "The linesman's in line, the referee's nearby. There were about three of them that were clear as anything and I can't understand why they weren't given."
Fellow midfielder Michael Ballack, who was booked for running 40 yards alongside Ovrebo to protest over the final penalty appeal being dismissed, said: "Everybody saw it and it was not one or two decisions, there were at least three, four five maybe we can discuss.
Hiddink unhappy with penalty decisions
"It was not just the last-minute decision. If you have the history of the situations before maybe he should give this one at least."
Chelsea manager Guus Hiddink supported his players for their actions and revealed he would stand by them.
"I can fully understand in the emotion of the game, as long as they don't touch him, I can fully understand this disappointment," he said of his players' reactions to the referee's rulings.
"It's not just one decision in doubt but it's several.
"I can fully understand and I protect my players for this when they have this emotion, just with loads of energy and adrenalin in their bodies."
In 2005, Swedish referee Anders Frisk was heavily criticised by then Chelsea boss Jose Mourinho after Drogba was controversially sent off in the first leg of a last-16 Champions League tie against Barcelona, which the Spanish side won 2-1.
Frisk then received death threats and subsequently decided to retire from the game.
At the time, Chelsea issued a statement condemning the actions of those who had abused Frisk.
Police in Ovrebo's home city of Oslo said they would be vigilant over any threats made against the referee.
An Oslo police spokesman said: "We are watching closely what is being posted on the internet. Anything we believe would threaten his personal safety will be taken seriously."
Former Uefa ref Graham Poll was quick to dismiss any suggestion that the governing body had influenced Ovrebo to ensure Barcelona reached the final on 27 May against Manchester United.
He told the BBC: "I refereed in Uefa for 13 years, 11 in their top group of referees, and never, ever, ever was there any suggestion of 'it would be nice if this team won' or 'could you do this team a favour' - I promise you, absolutely nothing.
"I'm 99.9% certain that there was nothing untoward going on here."
Poll added: "Tom had a bad day at work and, unfortunately, for a referee that gets highlighted.
"Irrespective of that, you can't possibly condone the behaviour of the Chelsea players at the final whistle and even before that."
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