Drogba was sent off early in the second half of his team's 2-1 defeat at the Nou Camp for a second bookable offence and Chelsea boycotted the post-match news conference.
"I would like to apologise to Mr Frisk if I might have, in any way, prompted him to end his refereeing career," the Ivory Coast striker told French television channel TF1 on Sunday.
"I really hope he will change his mind. Soccer needs great referees and Mr Frisk is one of them.
"Everyone makes mistakes and referees are human, we have to accept that", he added.
Frisk retired after receiving death threats from fans following criticism by Chelsea manager Jose Mourinho over his handling of the knockout-round first-leg tie.
Mourinho said his Barcelona counterpart Frank Rijkaard had talked to Frisk at halftime in the match.
Chelsea won the second leg 4-2 in London on March 8 to claim a place in the quarter-finals with a 5-4 aggregate victory.
Frisk announced his retirement four days later, saying he and his family had received death threats. The move caused furore in the European game, with Mourinho being branded "an enemy of football" by UEFA refereeing chief Volker Roth.
The Swede said on Saturday he would not go back on his decision despite efforts by UEFA and the game's worldwide body FIFA to persuade him to change his mind.
In an interview with the Sunday Times, Frisk described the period after the game in Barcelona as "the worst 16 days of my life".
Without naming Mourinho directly, Frisk was quoted as saying: "He violated my integrity.
"When you attack something that is so important to refereeing and so important to my culture, as well as to this fantastic hobby I have had for the last 26 years, of course you (inflict) hurt."
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